Aphasia is an acquired disorder caused by damage, most commonly due to stroke, to brain regions involved in speech and language. While language impairment is the defining symptom of aphasia, the co-occurrence of non-language cognitive deficits and their importance in predicting rehabilitation and recovery outcomes is well documented. However, people with aphasia (PWA) are rarely tested on higher-order cognitive functions, making it difficult for studies to associate these functions with a consistent lesion correlate. Broca's area is a particular brain region of interest that has long been implicated in speech and language production. Contrary to classic models of speech and language, cumulative evidence shows that Broca's area and surrounding regions in the left inferior frontal cortex (LIFC) are involved in, but not specific to, speech production. In this study we aimed to explore the brain-behaviour relationships between tests of cognitive skill and language abilities in thirty-six adults with long-term speech production deficits caused by post-stroke aphasia. Our findings suggest that non-linguistic cognitive functions, namely executive functions and verbal working memory, explain more of the behavioural variance in PWA than classical language models imply. Additionally, lesions to the LIFC, including Broca's area, were associated with non-linguistic executive (dys)function, suggesting that lesions to this area are associated with non-language-specific higher-order cognitive deficits in aphasia. Whether executive (dys)function - and its neural correlate in Broca's area - contributes directly to PWA's language production deficits or simply co-occurs with it, adding to communication difficulties, remains unclear. These findings support contemporary models of speech production that place language processing within the context of domain-general perception, action and conceptual knowledge. An understanding of the covariance between language and non-language deficits and their underlying neural correlates will inform better targeted aphasia treatment and outcomes