Heat 1 tablespoon oil in a large skillet over medium-low heat; whisk in flour, and cook until flour turns from white to a nutty brown color, 2 to 3 minutes. Stir in onion and cook until transparent, about 5 minutes. Add meats and brown until no longer pink, 10 to 12 minutes; stir in Cajun seasoning and garlic powder; drain fat. Cool to room temperature.
On a lightly floured surface, roll out the dough to a thickness of 1/4 inch. Use a 5 inch diameter round cookie cutter or cut around a saucer to make a round of dough. Place a heaping tablespoon of meat filling in the center of each round. Fold dough over filling and seal edges closed by pressing with a fork or fingers. Repeat to make 15 pies, re-rolling dough scraps as needed.
Heat oil for frying in deep fryer to 375 degrees F (190 degrees C).
Deep fry pies in small batches until golden brown, 3 to 4 minutes. Drain on paper towels. Or bake pies on greased cookie sheets in preheated 350 degree F (175 degrees C) oven 15 to 20 minutes, or until golden brown.