Preheat oven to 400 degrees F. Line 2 baking sheets with parchment paper, set aside.
In a medium bowl combine mashed potatoes and green bean casserole. Stir in Mexican seasoning and 1/4 cup of the cheese and set aside.
Unroll pie dough, 1 at a time. Use a 3-inch round cutter, dusted with flour and cut out as many rounds as possible (about 10 to 12) of the pie dough. Repeat with second pie dough.
Beat the egg lightly in a small bowl, set aside.
To assemble empanadas, fill the center of each round with 1/2 tablespoon of the mashed potatoes and green bean casserole mixture. Brush half of the perimeter of each dough round with the egg wash. Fold over 1 side of the round to make a half circle. Crimp the edges of each empanada with tines of a fork.
Place empanadas on prepared baking sheets. Brush each top lightly with egg wash and sprinkle each with a little of the remaining cheese.
Bake in preheated oven for 18 to 20 minutes or until golden brown.