Combine 3 tablespoons olive oil and next 4 ingredients in a large bowl; toss well. Spread squash mixture in a 15- x 10-inch jellyroll pan coated with cooking spray. Bake at 450º for 15 minutes; stir squash, and bake 5 more minutes. Set aside.
Heat 3 tablespoons butter and remaining 2 tablespoons olive oil in a large skillet over medium heat until butter melts. Add onion, and cook 20 minutes or until caramelized, stirring often.
Melt remaining 4 tablespoons butter in a small heavy saucepan over low heat; whisk in 1/4 cup flour until smooth. Cook 1 minute, whisking constantly. Gradually whisk in milk; cook over medium heat, whisking constantly, until mixture is thickened and bubbly. Stir in nutmeg. Stir sauce and squash mixture into onion mixture. Let cool.
Combine remaining 5 cups flour, shortening, and 2 teaspoons salt using a fork or pastry blender until mixture is crumbly. (Mixture should have small lumps.) Sprinkle 2/3 cup ice water, 1 tablespoon at a time, evenly over surface; stir with a fork until dry ingredients are moistened. Shape into a ball; roll out dough to 1/8-inch thickness on a lightly floured surface. Cut dough into 4-inch circles. Place about 2 tablespoons squash mixture in center of each dough circle. Moisten edges of dough with water. Fold dough over filling, and pinch to seal. Place on a foil-lined baking sheet.
Bake at 450º for 18 minutes or until golden.
Note: You may use thawed frozen empanada dough instead of the homemade pastry, if desired.