Preheat the broiler. Season the eggplant and zucchini with salt. Heat 1 tablespoon olive oil in a large ovenproof skillet over medium-high heat. Add the eggplant in one layer and cook until browned, about 2 minutes per side. Transfer to paper towels. Add another 1 tablespoon olive oil, then repeat with the zucchini.
Season the turkey with salt and dredge lightly in flour. Heat the remaining 1 tablespoon olive oil in the skillet, then add the turkey and cook until browned, about 2 minutes per side. Transfer to a plate.
Heat 1 tablespoon butter in the skillet. Add the tomatoes; when they sizzle, add the wine and bring to a boil. Add 1/4 teaspoon salt. Return the turkey to the skillet; arrange the eggplant, zucchini and basil on the cutlets and spoon the tomatoes on top. Top with the mozzarella and parmesan. Cut the remaining 1 tablespoon butter into pieces and add to the skillet. Simmer until the turkey is cooked through, about 3 minutes. Transfer to the broiler; cook about 1 minute.