Step 1Heat the oven to 275 degrees.
Step 2Heat the vegetable oil in a large skillet over medium-low to medium heat. Add the onion, red, yellow and green peppers and the herb sachet, season with salt and pepper, and cook until the vegetables are softened but not browned, 15 minutes. Remove the sachet and spread the mixture in an even layer in a 12-inch ovenproof skillet or round baking dish.
Step 3Arrange the sliced zucchini, eggplant, squash and tomatoes over the onion and peppers, beginning at the outside of the pan and working toward the center, alternating and overlapping them.
Step 4Mix the garlic, olive oil, thyme and salt and pepper to taste and sprinkle over the vegetables. Cover with foil, crimping the edges to seal, or with a tight-fitting lid, and bake for 2 1/2 hours.
Step 5Remove the lid and check the vegetables (the eggplant will take the longest to cook): They should have softened and be almost cooked. Return to the oven, uncovered, and cook until very tender, an additional 30 minutes. The byaldi can be served immediately or cooled to room temperature and then refrigerated until ready to use, preferably within a day or two.