Rinse the zucchini and yellow squash, quarter lengthwise, and then cut into 1-inch pieces. Rinse peppers and dice to 1 inch; set aside. Peel the shallots and finely dice; mince the garlic. Rinse the tomatoes, cut in half, and remove seeds. Coarsely chop and set aside with juices. Set a casserole in the oven, add oil, and heat. Add shallots and cook for about 3 minutes, or until lightly browned and softened. Add garlic and cook for 1 minute. Do not burn. Add basil, stirring to heat, coat, and infuse oil. Add squash and peppers and cook for about 6–8 minutes. Vegetables should be lightly browned but still firm. Add tomatoes with their juices and salt. Cook uncovered for about 10–15 minutes. Sauce should be slightly thickened and the vegetables softened. Pull casserole forward in the oven. Use a ladle to make an indentation in the vegetables for each egg. Crack eggs one at a time into a small bowl and slide into indentation. Cover casserole and return to oven for about 8–10 minutes, or until eggs have set. Sprinkle with Parmigiano-Reggiano, pepper flakes, and black pepper. Ladle eggs with plenty of vegetable sauce in individual bowls to serve.