In a large bowl, combine carrots and fennel. Add the 1 tablespoon oil, the salt, and pepper; toss to coat.
Place a large skillet or wok on grill side burner. In the skillet, heat the 2 tablespoons olive oil over medium heat. Add vegetable mixture and cook for 15 to 20 minutes or until vegetables are tender, stirring occasionally. Remove pan from heat. Gradually add spinach to skillet, tossing until spinach wilts.
Transfer vegetable mixture to a serving plate. Sprinkle with Parmesan cheese, if desired. Makes 4 to 6 servings.