Unroll pie crusts onto a flat surface. Top each quadrant of crust with 1/2 cup of beef, 1/4 cup of cheese and about a tablespoon of chiles, making even layers and spreading ingredients to within 1/2-inch of the edges. Top with second pie crust. Using a pastry cutter or sharp knife, make an X across the circle, making 4 equal sections. Pinch around the edges with a fork to seal.
Transfer empanadas to a baking sheet and make small slits in the top of each one to allow steam to escape during cooking. Bake 8 to 10 minutes, until crust is golden brown.