The present disclosure is directed to a combustion system including a panel fuel injector. The panel fuel injector includes a first side wall, a second side wall, and an aft wall. The first side wall and the second side wall are interconnected by the aft wall. The panel fuel injector further includes a cooling air plenum that is defined between the first side wall and the second side wall. The aft wall defines a plurality of cooling holes in fluid communication with the cooling air plenum. One or more of the cooling holes of the plurality of cooling holes is oriented towards at least one of a leading edge, a pressure side wall, or a suction side wall of a stationary nozzle disposed proximate to the aft end wall.