On a half-sheet pan or other large, rimmed baking sheet, arrange the vegetables in a single layer. Place the tomatoes on the lower oven rack and the vegetables on the upper rack. Set the timer for 20 minutes.
In a large mixing bowl, combine the diced eggplant, zucchini, yellow squash, bell pepper and onion. Whisk together ¼ cup olive oil, the balsamic vinegar, garlic, salt, a few generous twists black pepper and a pinch of red pepper flakes. Drizzle it over the vegetables and toss with your hands or a large spoon until the vegetables are evenly coated.
Preheat oven to 425 degrees Fahrenheit with two racks in the middle positions. On a quarter pan or small baking dish, toss the whole baby tomatoes with 2 tablespoons olive oil and a sprinkle of salt and pepper. Set aside.