Executive functions refer to high-level cognitive processes that, by operating on lower-level mental processes, flexibly regulate and control our thoughts and goal-directed behavior. Despite their crucial role, the study of the nature and organization of executive functions still faces inherent difficulties. Moreover, most executive function models put under test until now are brain-free models: they are defined and discussed without assumptions regarding the neural bases of executive functions. By using a latent variable approach, here we tested a brain-centered model of executive function organization proposing that two distinct domain-general executive functions, namely, criterion setting and monitoring, may be dissociable both functionally and anatomically, with a left versus right hemispheric preference of prefrontal cortex and related neural networks, respectively. To this end, we tested a sample of healthy participants on a battery of computerized tasks assessing criterion setting and monitoring processes and involving diverse task domains, including the verbal and visuospatial ones, which are well-known to be lateralized. By doing this, we were able to specifically assess the influence of these task domains on the organization of executive functions and to directly contrast a process-based model of EF organization versus both a purely domain-based model and a process-based, but domain-dependent one. The results of confirmatory factor analyses showed that a purely process-based model reliably provided a better fit to the observed data as compared to alternative models, supporting the specific theoretical model that fractionates a subset of executive functions into criterion setting and monitoring with hemispheric specializations emerging regardless of the task domain.