The emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants that escape convalescent and vaccine-induced antibody responses has renewed focus on the development of broadly protective T-cell-based vaccines. Here, we apply structure-based network analysis and assessments of HLA class I peptide stability to define mutationally constrained CD8+ T cell epitopes across the SARS-CoV-2 proteome. Highly networked residues are conserved temporally among circulating variants and sarbecoviruses and disproportionately impair spike pseudotyped lentivirus infectivity when mutated. Evaluation of HLA class I stabilizing activity for 18 globally prevalent alleles identifies CD8+ T cell epitopes within highly networked regions with limited mutational frequencies in circulating SARS-CoV-2 variants and deep-sequenced primary isolates. Moreover, these epitopes elicit demonstrable CD8+ T cell reactivity in convalescent individuals but reduced recognition in recipients of mRNA-based vaccines. These data thereby elucidate key mutationally constrained regions and immunogenic epitopes in the SARS-CoV-2 proteome for a global T-cell-based vaccine against emerging variants and SARS-like coronaviruses.