Preheat oven to 375 degrees F. Spray a baking sheet with nonstick cooking spray; set aside.
Heat oil in a large skillet over medium-high heat. Add onion and peppers and cook for 3 minutes, or until tender. Add turkey and cook, breaking up, for 6-8 minutes or until cooked through.
Season with salt, pepper, cumin, paprika and garlic powder. Add chicken broth and tomato paste and mix until combined. Let simmer for 3-5 minutes or until most of the liquid is evaporated; remove from heat and set aside.
In a mixing bowl or stand mixer, combine self rising flour and Greek yogurt until a thick dough forms. Divide dough into 8 equal pieces (approximately 4.9 ounces each) and roll out onto a lightly floured surface until 6-8 inches in diameter.
Divide turkey mixture evenly between dough (approximately 4.7 ounces each) and top each with 1 Tablespoon of cheese. Fold dough over the top to form a half circle, press edges shut with your hand then use a fork to crimp and secure the edge of each empanada.
Place empanadas on prepared pan, then whisk egg and brush on the top and sides. Bake for 25-30 minutes or until golden brown.