Most existing studies characterizing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-specific T cell responses are peptide based. This does not allow evaluation of whether tested peptides are processed and presented canonically. In this study, we use recombinant vaccinia virus (rVACV)-mediated expression of SARS-CoV-2 spike protein and SARS-CoV-2 infection of angiotensin-converting enzyme (ACE)-2-transduced B cell lines to evaluate overall T cell responses in a small cohort of recovered COVID-19 patients and uninfected donors vaccinated with ChAdOx1 nCoV-19. We show that rVACV expression of SARS-CoV-2 antigen can be used as an alternative to SARS-CoV-2 infection to evaluate T cell responses to naturally processed spike antigens. In addition, the rVACV system can be used to evaluate the cross-reactivity of memory T cells to variants of concern (VOCs) and to identify epitope escape mutants. Finally, our data show that both natural infection and vaccination could induce multi-functional T cell responses with overall T cell responses remaining despite the identification of escape mutations.