Preheat oven to 375°F.
Slice the eggplant, zucchini, squash, and tomatoes into ⅛-inch slices using a food processor with a 3mm blade. (See Tip 6)
Place the eggplant, zucchini, squash, and tomato slices in a single layer on doubled layers of paper towels. Sprinkle each with ½ teaspoon of Kosher salt. Allow to sit for 30 minutes to help extract excess moisture. (See Tip 7)
After 30 minutes, blot the veggies with additional paper towels.
Heat 2 tablespoons of olive oil over medium heat in a 10-inch oven-safe braiser or skillet. Add onions, bell pepper, remaining ¼ teaspoon of salt, and pepper. Sauté for 8 to 10 minutes or until softened. Add garlic, basil, and 1 ½ tablespoons of thyme. Stir to combine and cook until fragrant, about 30 seconds.
Add the tomato puree; stir to combine. Cook uncovered for 10 minutes, or until thickened.
Stir in the vinegar and remove from the heat. Spread in an even layer on the bottom of the pan.
Arrange the eggplant, zucchini, yellow squash, and Roma tomatoes in concentric circles on top of the sauce. Start at the outer edge of the pan and work inward, alternating the vegetables and overlapping the slices so that just a little bit of each slice is visible. May be prepared in advance up to this point. (See Tip 8)
Drizzle the remaining 2 tablespoons of the olive oil over the vegetables. Sprinkle the remaining 1 ½ teaspoons of thyme over the top.
Cover with a tight-fitting lid or aluminum foil. Bake in a preheated 375°F oven until the vegetables are softened but are not browned around the edges, 40 to 45 minutes. Uncover and let sit for 5 minutes before serving. Garnish with torn basil leaves if desired.
Yield: 4 to 6 servings. (See Tip 9)