Position rack in center of oven. Heat oven to 350 degrees F. Generously butter 9-inch round baking dish.
Heat in large, heavy skillet over medium-high heat unsalted butter and olive oil. Add and cook, stirring, for 3 minutes, onion, sweet red pepper, and small red-skinned new potatoes.
Stir in and cook until vegetables are partially softened but not browned, about 2 minutes. Add 2 large cloves garlic, minced. Add and cook, stirring until almost tender, 4 to 5 minutes, yellow squash and zucchini.
Toss together in large bowl cornmeal, flour, grated Parmesan cheese fresh thyme leaves, salt and black pepper.
In separate bowl, whisk together milk and eggs.
Whisk egg mixture into cornmeal mixture until combined. Stir vegetables into the loose batter and spread evenly in prepared baking dish. Bake until firm, 25 to 30 minutes.
Remove from oven and sprinkle with with 6 tablespoons grated Gruyere cheese (about 2 ounces). Return to oven and bake until golden around edges and cheese is melted, about 7 minutes more. Serve casserole hot or at room temperature. Makes 4 servings.
