Cut bell pepper in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 8 minutes or until blackened. Place in a paper bag; fold to close tightly. Let stand 10 minutes. Peel and cut into strips.
While bell pepper broils, bring 10 cups water to a boil in a Dutch oven. Add carrots and onions; cook 2 minutes. Add peas; cook 2 minutes. Drain; rinse with cold water. Drain. Remove carrot skins by rubbing gently with a clean, dry paper towel. Remove stem ends from onions; peel.
Heat a large nonstick skillet over medium-high heat. Add 2 tablespoons olive oil, and swirl to coat. Add onions, mushrooms, and fennel; sauté for 2 minutes, stirring occasionally. Add 1/4 teaspoon salt; reduce heat to medium, and sauté for 3 minutes, stirring occasionally. Add bell pepper, carrots, and vinegar; cook 2 minutes or until liquid almost evaporates.
Cook pasta in boiling water 2 minutes; drain. Combine pasta, remaining 2 tablespoons oil, remaining 1/2 teaspoon salt, fennel mixture, capers, and crushed red pepper in a large bowl; toss to combine. Add mozzarella; sprinkle with thyme.
MyRecipes is working with Let's Move!, the Partnership for a Healthier America, and USDA's MyPlate to give anyone looking for healthier options access to a trove of recipes that will help them create healthy, tasty plates. For more information about creating a healthy plate, visit www.choosemyplate.gov.