Let piecrusts stand at room temperature for 20 minutes. Unfold crusts. Cut into 16 to 18 four-inch circles, rerolling as necessary. Set aside.
Finely chop chicken. Set aside.
For filling, pour the 1 tablespoon cooking oil into a large skillet. (Add more oil as necessary during cooking.) Preheat over medium-high heat. Stir-fry garlic in hot oil for 15 seconds. Add carrot and onion. Stir-fry for 2 minutes. Remove from skillet. Add the chicken and beef or pork. Stir-fry for 2 to 3 minutes or until no pink remains. Drain. Add curry powder; stir-fry 1 minute more. Return vegetables to the skillet. Stir in salt and pepper. Remove all ingredients from skillet and cool.
In a wok or 3-quart saucepan heat 1-1/2 to 2 inches of cooking oil or shortening to 365 degree F. Meanwhile place about 2 tablespoons of the filling in the center of each pastry circle. Fold the pastry over the filling, making half circles. Moisten the edges with water. Pinch to seal. Fry pastries, a few at a time, in hot oil for 3 to 5 minutes or until golden brown, turning once.
Using a wire strainer or slotted spoon, remove pastries from the oil. Drain on a wok rack or on paper towels. Keep warm in a 300 degree F oven while frying remaining pastries. Serve warm. Makes 16 to 18 appetizer servings.