To prepare filling, heat a large skillet over medium-high heat. Coat pan with cooking spray. Add turkey; cook 5 minutes or until browned, stirring to crumble. Stir in chili powder, cumin, 1/2 teaspoon salt, and pepper; cook 1 minute, stirring often. Stir in 1/2 cup water and tomato paste. Cook 2 minutes or until turkey mixture thickens. Remove from heat; stir in cheese. Place in a bowl, and cool to room temperature; cover and chill 30 minutes.
To prepare dough, lightly spoon flour into dry measuring cups; level with a knife. Place flour, baking powder, sugar, and 1/4 teaspoon salt in a food processor; pulse 2 times or until combined. Add chilled butter; pulse 4 times or until mixture resembles coarse meal. With processor on, add 3/4 cup ice water through the food chute, processing just until combined (do not form a ball). Turn the dough out onto a floured surface; knead lightly 4 times with floured hands.
Divide the dough into 24 portions. Working with 1 portion at a time (cover remaining portions to keep dough from drying), roll into a 3 1/2-inch circle on a floured surface. Spoon 1 rounded tablespoon turkey mixture onto half of circle. Fold dough over filling; press edges together to seal. Place on a large baking sheet. Repeat procedure with remaining dough and filling. Cover with plastic wrap; freeze until firm. Place in zip-top plastic bags; freeze for up to 3 months.
Preheat oven to 400º.
Place frozen empanaditas on 2 baking sheets coated with cooking spray. Bake at 400° for 30 minutes or until bottoms are golden brown and tops begin to brown. Serve warm.