New methods for the general asymmetric synthesis of sulfonimidamides are of great interest due to their applications in medicinal chemistry, agrochemical discovery, and academic research. We report a palladium-catalyzed cross-coupling method for the enantioselective aryl-carbonylation of sulfonimidamides. Using data science techniques, a virtual library of calculated bisphosphine ligand descriptors was used to guide reaction optimization by effectively sampling the catalyst chemical space. The optimized conditions identified using this approach provided the desired product in excellent yield and enantioselectivity. As the next step, a data science-driven strategy was also used to explore a diverse set of aryl and heteroaryl iodides, providing key information about the scope and limitations of the method. Furthermore, we tested a range of racemic sulfonimidamides for compatibility of this coupling partner. The developed method offers a general and efficient strategy for accessing enantioenriched sulfonimidamides, which should facilitate their application in industrial and academic settings.