A method of manufacturing a cooled gas turbine component includes forming a core with an outer surface. The outer surface includes a core feature. The method also includes casting an outer wall of an airfoil about the core. The outer wall has an exterior surface and an interior surface. The interior surface includes a shaped inlet portion that corresponds to the core feature. Moreover, the method includes forming an outlet portion through the outer wall to fluidly connect the outlet portion to the shaped inlet portion. The shaped inlet portion and the outlet portion cooperatively define a cooling aperture through the outer wall.