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Step 1
In a large, heavy-bottomed pot (I use a 6.75-quart Dutch oven), add the olive oil and pancetta before heating the pot. Place over medium heat and cook for 3–4 minutes, just until the pancetta renders its fat but remains soft—not browned or crispy.
Step 2
Add the onions, celery, and carrots to the pot, along with 1/2 teaspoon each of kosher salt and freshly ground black pepper. Cook over medium heat, stirring occasionally, until the vegetables are tender but not caramelized, about 10–12 minutes (see note).
Step 3
Stir in the garlic, rosemary, thyme, and Italian seasoning, and cook for about 1 minute, until fragrant.
Step 4
Stir in the crushed tomatoes (with their juices/purée), followed by the cannellini beans, kidney beans, zucchini, and green beans.
Step 5
Pour in 6 cups of broth or stock and stir until well combined. Add the bay leaf and Parmigiano Reggiano rind.
Step 6
Bring the soup to a boil, cover the pot, and reduce the heat to maintain a gentle simmer. Cook, covered, for 20–25 minutes, until the vegetables are tender. Stir the soup a couple of times as it simmers.
Step 7
Uncover the pot and stir the soup. Add the pasta and simmer uncovered for about 10 minutes, until the pasta is tender, stirring occasionally to make sure the pasta isn't sticking to the pot.
Step 8
Remove and discard the Parmigiano Reggiano rind and bay leaf. If the soup is too thick, stir in additional broth or stock, 1/2 cup at a time, until you reach your desired consistency. The amount needed may vary by batch.
Step 9
Taste and adjust seasoning with salt and pepper as needed. Roughly tear the fresh basil leaves and stir them into the soup just until wilted.
Step 10
Ladle the soup hot into bowls. Finish with a drizzle of extra virgin olive oil, a generous sprinkle of grated Parmigiano Reggiano, and a few grinds of black pepper. For a spicy kick, add a few crushed red pepper flakes. Serve with crusty Italian bread for dipping.