Combine masa harina, flour, cornmeal, baking powder, Southwest seasoning, salt and 3 turns pepper in a medium bowl and mix thoroughly. Cream in shortening with a fork until mixture resembles coarse crumbs. Add about 1 cup water, a little at a time, working dough until all water is completely incorporated. Use just enough water to make dough come together. Turn dough out onto a lightly floured surface and pat into a 12- by 3-inch log. Refrigerate until firm, about 20 minutes.
Preheat oven to 375 degrees F. Remove dough from refrigerator and divide log into 4 equal sections, each about 3 inches long. Carefully roll out each section between sheets of plastic wrap to an 8-inch circle, about 1/4-inch thick. Handle dough with care to keep from cracking. Brush top sides of rounds with egg wash. Mound filling in center of each round and fold dough to form a half-moon shape. Crimp edges with a fork and brush with remaining egg wash. Transfer empanadas to a parchment or wax-paper-lined baking sheet and bake 35 minutes until golden.