An apparatus for drilling cooling holes through a wall of a hollow component is disclosed. First, a laser drill is used for drilling at least one rough blind hole within a component wall, for example a turbine airfoil, so as to retain a residual bottom plate portion. Next, an electro discharge machine (EDM), for example a rotating EDM or plunge EDM, is used for finishing at least one rough blind hole so as to create at least one finished hole and breaking through the bottom plate portion.