How to Make It
Whisk together milk, mustard, eggs, and 1 tablespoon of the oil in a large bowl. Whisk in all-purpose flour and whole-wheat flour until smooth. Let rest 15 minutes.
Preheat oven to 425°F. Place an 11- x 7-inch glass or ceramic baking dish in oven while it preheats.
Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high. Add onion wedges, cut sides down; cook 5 minutes turning once, or until lightly browned on both sides. Add eggplant; cook 5 minutes, stirring occasionally. Add bell pepper, zucchini, squash, thyme, pepper, and garlic. Cook, stirring occasionally, until squashes are slightly tender, about 5 minutes. Stir in tomatoes and salt; cook 3 minutes. Remove from heat.
Add butter and remaining 1 tablespoon oil to preheated baking dish. When butter has melted, pour batter in dish and top with vegetable mixture. Bake in preheated oven until set and lightly browned, 30 to 35 minutes. Remove from oven. Let stand 5 minutes. Sprinkle with basil.