Step 1

Heat oil in a Dutch oven over medium-high heat. Add onion, carrot, and celery. Cook, stirring occasionally, until vegetables begin to soften, about 5 minutes. Add garlic and cook, stirring frequently, 1 minute more.

Step 2

Stir in broth, beans, tomatoes, pasta, and tomato sauce. Bring to a boil. Reduce heat and simmer, covered until pasta is tender, about 20 minutes. Add peas and vinegar. Cook, uncovered, until peas are heated through, 2 to 3 minutes more. Season with salt and pepper. Serve soup topped with cheese.