Cut eggplant into 1⁄8-inch-thick slices. Sprinkle both sides with 1 teaspoon salt and place on a wire rack set over a rimmed sheet pan. Let stand for 20 to 30 minutes. (Salting the eggplant is optional but can remove excess bitterness.)
Pat dry with paper towels.
Preheat oven to 375°.
Heat 1 tablespoon oil in a deep cast iron or other ovensafe skillet over medium-high heat. Add onion, bell pepper, seasoning, and red pepper flakes. Cook, stirring frequently, for 5 minutes or until tender. Add garlic; cook 1 minute. Stir in smoked paprika, remaining 1 teaspoon salt, and pepper. Add canned tomatoes, basil, sugar (omit if using Pesto Sauce), and vinegar, stirring until well blended. Remove from heat.
Cut zucchini, yellow squash, and tomatoes into 1⁄8- to ¼-inch-thick slices. Arrange sliced vegetables, including reserved eggplant, in layers over sauce in skillet. Brush top of vegetables with remaining 2 tablespoons olive oil.
Cover with aluminum foil and bake for 35 to 40 minutes. Uncover and bake for 15 more minutes or until vegetables are tender. Let rest for 10 minutes. Drizzle with Pesto Sauce, if desired, and sprinkle with cheese.