Cook the pasta according to the package directions. Drain and reserve.
Meanwhile, cook the garlic, onion, carrot, salt, and black pepper in the olive oil in a large pot over medium until just tender, about 10 minutes. Add the bell pepper, zucchini, and grape tomatoes and cook until the vegetables are just tender, 5 minutes more. Add the broth. Bring to a boil; reduce heat to a simmer and cook for 10 minutes.
Stir in the pasta to warm and serve, garnished with shaved Parmesan and chopped parsley.
Easy Homemade Parmesan Broth
Combine 12 oz. Parmesan cheese rinds with 2 yellow onions (sliced), 3 medium carrots (peeled and sliced), 1 smashed garlic clove, and 4 bay leaves in a large pot. Add 5 quarts cold water. Bring to a boil. Reduce heat and simmer, stirring occasionally, until flavorful, 30 minutes. Strain and cool completely. Makes 4½ quarts (18 cups).