Preheat oven to 375°.
Heat olive oil in a large skillet over medium-high heat. Add onion; sauté 10 minutes or until tender and lightly browned. Add garlic; sauté 2 minutes. Add kale and spinach; sauté 8 minutes or until kale is tender. Stir in pepper, salt, and nutmeg. Remove from heat; cool slightly. Stir in feta.
Separate dough into 8 pieces. Roll each dough piece into a 5-inch circle. Spoon about 1/3 cup kale mixture on half of each circle, leaving a 1/2-inch border. Fold dough over kale mixture until edges almost meet. Bring bottom edge of dough over top edge; crimp edges of dough with fingers to form a rim.
Place turnovers on a baking sheet coated with cooking spray. Lightly coat turnovers with cooking spray; sprinkle each turnover with about 1 teaspoon Parmesan. Bake at 375° for 18 minutes or until golden brown. Let stand at least 5 minutes before serving; serve warm or at room temperature.