1. Preheat oven to 350°. Bring first 2 ingredients and water to cover to a boil in a Dutch oven over medium-high heat, and boil 5 minutes or until crisp-tender. Drain; gently press between paper towels.
2. Melt 2 Tbsp. butter in a skillet over medium-high heat; add onion, and sauté 10 minutes or until tender. Add garlic, and sauté 2 minutes.
3. Stir together squash, onion mixture, corn, next 6 ingredients, and 1/2 cup each breadcrumbs and Asiago cheese just until blended. Spoon mixture into a lightly greased 13- x 9-inch baking dish.
4. Melt remaining 2 Tbsp. butter. Stir in remaining 1 cup breadcrumbs and 1/2 cup Asiago cheese. Sprinkle over casserole.
5. Bake at 350° for 45 to 50 minutes or until golden brown and set. Let stand 15 minutes before serving.