Bring a large pot of lightly salted water to boil. Add pasta, and cook until al dente, about 8 to 10 minutes. Drain, pour pasta into a large bowl, and stir in 3 tablespoons olive oil, 2 tablespoons butter, Parmesan, and parsley.
Meanwhile, warm 1/2 cup olive oil and 3 tablespoons butter in a large skillet over medium heat. Stir in garlic.
Season chicken pieces with salt and pepper. In a bowl, whisk together the eggs and milk. Dip chicken into egg mixture, then coat with bread crumbs. Place chicken pieces and limes into hot skillet. Cover, and cook until chicken is well browned on the bottom. Turn the chicken, and pour wine into the skillet; cover, and cook until the chicken is browned. Stir in diced tomatoes; cover, and cook about 3 minutes. Remove lime wedges, and serve over pasta.
