Heat 1 teaspoon oil in skillet over medium heat. Cook carrots, basil, salt and spinach in oil about 2 minutes, stirring occasionally. Remove vegetable mixture from skillet.
Mix together cooked pasta, eggs, ricotta cheese, Parmesan cheese and pepper. Heat 1 teaspoon oil in skillet over medium-high heat. Drop pasta mixture by 1/2 cup mounds into the hot oil. Cook patties in oil 6 to 8 minutes, turning after 4 minutes, until golden brown.