We investigated the design and analysis of observational booster vaccine effectiveness (VE) studies by performing a scoping review of booster VE literature with a focus on study design and analytic choices. We then applied 20 different approaches, including those found in the literature, to a single dataset from Michigan Medicine. We identified 80 studies in our review, including over 150 million observations in total. We found that while protection against infection is variable and dependent on several factors including the study population and time period, both monovalent boosters and particularly the bivalent booster offer strong protection against severe COVID-19. In addition, VE analyses with a severe disease outcome (hospitalization, intensive care unit admission, or death) appear to be more robust to design and analytic choices than an infection endpoint. In terms of design choices, we found that test-negative designs and their variants may offer advantages in statistical efficiency compared to cohort designs.