Heat the olive oil in a large skillet. Add the onion and garlic and sauté until soft, about 5-8 minutes.
Add the turkey, gravy and mashed potatoes and stir until heated through and combined.
Fold in cranberry sauce and 2 tablespoons parsley.
Unroll the pie doughs and using a 5-inch round cutter, cut circles out (about 10). Place about 1 1/2 tablespoon of filing in the center of each circle. Brush around the edges of each circle with the beaten egg and fold the dough over the filling, pressing the edges with a fork. Repeat with all the dough circles.
Place the empanadas on a baking sheet, brush with beaten egg wash and bake for 15 minutes.
While the empanadas bake mix the sour cream, remaining parsley, chives, and thyme in a small bowl. Serve the empanadas warm with a dollop of herbed dip.