As SARS-CoV-2 variants continue to emerge capable of evading neutralizing antibodies, it has become increasingly important to fully understand the breadth and functional profile of T cell responses to determine their impact on the immune surveillance of variant strains. Here, sampling healthy individuals, we profiled the kinetics and polyfunctionality of T cell immunity elicited by mRNA vaccination. Modeling of anti-spike T cell responses against ancestral and variant strains of SARS-CoV-2 suggested that epitope immunodominance and cross-reactivity are major predictive determinants of T cell immunity. To identify immunodominant epitopes across the viral proteome, we generated a comprehensive map of CD4+ and CD8+ T cell epitopes within non-spike proteins that induced polyfunctional T cell responses in convalescent patients. We found that immunodominant epitopes mainly resided within regions that were minimally disrupted by mutations in emerging variants. Conservation analysis across historical human coronaviruses combined with in silico alanine scanning mutagenesis of non-spike proteins underscored the functional importance of mutationally-constrained immunodominant regions. Collectively, these findings identify immunodominant T cell epitopes across the mutationally-constrained SARS-CoV-2 proteome, potentially providing immune surveillance against emerging variants, and inform the design of next-generation vaccines targeting antigens throughout SARS-CoV-2 proteome for broader and more durable protection.