A good place to start is this scoping review, which provides an 
overview of how competency frameworks have been developed in the health 
professions since the 1970s:
- Batt, A.M., Tavares, W., Williams, B. The development of competency frameworks in healthcare professions: a scoping review. Advances in Health Sciences Education. 2020;25(4):913-987. 10.1007/s10459-019-09946-w. Publisher link.
Next, two systematic reviews from Breanna Lepre and Nicole Murray, 
which explore the role of stakeholders in developing competency 
frameworks, and specifically patients and the public:
- Lepre B, Palermo C, Mansfield KJ and Beck EJ (2021) Stakeholder 
 Engagement in Competency Framework Development in Health Professions: A
  Systematic Review.  Frontiers in Medicine: Healthcare Professions Education. 8:759848. doi: 10.3389/fmed.2021.759848 Publisher link
- Murray,
 N., Palermo, C. Batt, A.M., Bell, K. Does patient and public 
involvement influence development of competency frameworks in the health
 professions? A systematic review. Frontiers in Medicine: Healthcare Professions Education. 2022, Jul.10.3389/fmed.2022.918915. [Q1]. Publisher link.  
Next up, a conceptual framework which utilises systems thinking to 
structure exploration and understanding of practice, which we suggest is
 complex and contextual:
- Batt, A.M., Williams, B., Brydges, M., Leyenaar, M., Tavares, W.
 New ways of seeing: supplementing existing competency framework 
development guidelines with systems thinking. Advances in Health Sciences Education. 2021;26(4):1355-1371. 10.1007/s10459-021-10054-x. Publisher link.
Now armed with these historical perspectives and awareness of gaps in
 current approaches, comes the practical “how to make a competency  
framework” publication. This paper provides a synthesis of existing 
development guidance, combined with the conceptual framework outlined 
above, and a furthering of knowledge informed by mixed-methods research 
approaches, approaches to qualitative “rigour”, and other developments:
- Batt, A.M., Williams, B., Rich, J., Tavares, W. A six-step model
 for developing competency frameworks in the healthcare professions. Frontiers in Medicine: Healthcare Professions Education. 2021, Dec. 10.3389/fmed.2021.789828. Publisher link
If you wish to read the existing guidance on developing frameworks, 
there is a summary table provided in the first scoping review (Table 1, 
p915-917). 
Specific guidance on methods that may be used during the development 
process is often generic base don method, however, specific insights 
from the competency framework development process are beginning to 
emerge:
- Allen L, Palermo C. Using Document Analysis to Develop 
Competency Frameworks: Perspectives from the revision of Competency 
Standards for Dietitians. Frontiers in Medicine: Healthcare Professions Education. Publisher link.
- 
 Ash, Susan, Kerryn Dowding, and Susan Phillips. ‘Mixed Methods Research
 Approach to the Development and Review of Competency Standards for 
Dietitians’. Nutrition & Dietetics 68, no. 4 (2011): 305–15. https://doi.org/10.1111/j.1747-0080.2011.01552.x.    
- Palermo,
 Claire, Jane Conway, Eleanor J. Beck, Janeane Dart, Sandra Capra, and 
Susan Ash. ‘Methodology for Developing Competency Standards for 
Dietitians in Australia’. Nursing & Health Sciences 18, no. 1 (March 2016): 130–37. https://doi.org/10.1111/nhs.12247.
- Arakawa,
 Naoko, and Lina R. Bader. ‘Consensus Development Methods: 
Considerations for National and Global Frameworks and Policy 
Development’. Research in Social and Administrative Pharmacy, 30 June 2021. https://doi.org/10.1016/j.sapharm.2021.06.024.   
- Scodras,
 Stephanie, Kyla Alsbury-Nealy, Heather Colquhoun, Euson Yeung, Susan B.
 Jaglal, and Nancy M. Salbach. ‘Methodological Approaches for 
Identifying Competencies for the Physiotherapy Profession: A Scoping 
Review’. Discover Education 1, no. 1 (28 June 2022): 9. https://doi.org/10.1007/s44217-022-00008-9.     
Generic methodological guidance that may be useful includes:
- Delphi: Trevelyan, Esmé G, and Nicola Robinson. ‘Delphi Methodology in Health Research: How to Do It?’ European Journal of Integrative Medicine, Diagnostic Techniques and Outcome Measures for Integrated Health, 7, no. 4 (1 August 2015): 423–28. https://doi.org/10.1016/j.eujim.2015.07.002.
- Mixed
 methods data integration: O’Cathain, Alicia, Elizabeth Murphy, and Jon 
Nicholl. ‘Three Techniques for Integrating Data in Mixed Methods 
Studies’. BMJ (Online) 341, no. 7783 (2010): 1147–50. https://doi.org/10.1136/bmj.c4587.    
- Mixed
 methods: Creswell, John W, A Klassen, V Plano Clark, and Katherine 
Smith. ‘Best Practices for Mixed Methods Research in the Health 
Sciences’, 2014. https://doi.org/10.1002/cdq.12009.    
- Reviews:
    Grant, Maria J, and Andrew Booth. ‘A Typology of Reviews: An 
Analysis of 14 Review Types and Associated Methodologies.’ Health Information and Libraries Journal 26, no. 2 (2009): 91–108. https://doi.org/10.1111/j.1471-1842.2009.00848.x.    
- Rapid/restrictred
 reviews: Tricco, Andrea C., Hanan Khalil, Cheryl Holly, Garumma 
Feyissa, Christina Godfrey, Catrin Evans, Diane Sawchuck, et al. ‘Rapid 
Reviews and the Methodological Rigor of Evidence Synthesis: A JBI 
Position Statement’. JBI Evidence Synthesis, 4 March 2022. https://doi.org/10.11124/JBIES-21-00371.    
- Curriculum
 mapping:    Watson, Eilean Genevieve S., Carole Steketee, Kylie 
Mansfield, Maxine Moore, Bronwen Dalziel, Arvin Damodaran, Ben Walker, 
Robbert J. Duvivier, and Wendy Hu. ‘Curriculum Mapping for Health 
Professions Education: A Typology’. Focus on Health Professional Education: A Multi-Professional Journal 21, no. 1 (30 April 2020): 91. https://doi.org/10.11157/fohpe.v21i1.364.    
Reporting of the development process has historically been lacking in  detail required to make decisions around utility and validity. The  CONFERD-HP  recommendations for reporting COmpeteNcy FramEwoRk Development in health professions provides an  outline of the essential items that should be reported when discussing  the development of a competency framework in the health professions.
- Alan M Batt, Walter Tavares, Tanya Horsley, Jessica V Rich, Brett  Williams, the CONFERD-HP Collaborators, CONFERD-HP: recommendations for  reporting COmpeteNcy FramEwoRk Development in health professions,  British Journal of Surgery, 2022;, znac394, https://doi.org/10.1093/bjs/znac394