Stroke is the leading cause of long-term disability worldwide. Incurred brain tissue damage disrupts cognition, often with persisting deficits in language and executive capacities. Yet, despite their clinical relevance, the commonalities, and differences of impairments in language versus executive functions remain under-specified. To fill this gap, we tailored a Bayesian hierarchical modeling solution in a largest-of-its-kind clinical cohort (1080 stroke patients) to deconvolve language and executive control in the brain substrates of stroke insults. Individual deficits were characterized by a rich neuropsychological test battery. Bayesian modeling predicted interindividual differences in eight cognitive outcome scores 3 months after stroke based on specific tissue lesion topologies. We identified unique anterior-posterior and left-right principles that underlie the impairment of both cognitive functions due to distributed lesion patterns. A factor analyses extracted four distinct cognitive factors that distinguished left- and right-hemispheric contributions to ischemic tissue lesion. Language was primarily affected by lesions to prefrontal and temporal regions in the left hemisphere, while executive control impairments were preferentially linked to damage of occipital and postcentral regions in the right hemisphere. The interplay of both cognitive dimensions was reflected in two distinct factors, tracking executive speech functions and verbal memory capacities. Impairments on these two cognitive factors were mainly linked to left-hemispheric lesion atoms, with only minor contributions of right-hemispheric regions. These identified left-hemispheric regions covered pre- and postcentral regions associated with cognitive control as well as motor cortices. Zooming in on specific lesion topologies across the whole brain provided a fine-grained picture of impairment dimensions associated with distinct lesion atom patterns and specific brain regions for each identified cognitive factor. The identified factors also differed in their overlap with language and executive control networks. These findings shed light onto the causal implications of hemispheric specialization for human cognition; and make steps towards subgroup-specific treatment protocols to benefit stroke patients.