Ingredients

• 2 tablespoons extra-virgin olive oil, plus more for serving

• 2 tablespoons unsalted butter

• 2 leeks, white and light green parts only, rinsed and diced

• 2 cloves garlic, roughly chopped

• 2 teaspoons salt, divided

• Ground pepper to taste

• 1 pound potatoes, diced (1/2-inch)

• 3 medium carrots, sliced 1/4-inch thick

• 4 celery stalks, sliced 1/4-inch thick

• 2 medium yellow squash, halved lengthwise and sliced 1/4-inch thick

• 1 medium zucchini, halved lengthwise and sliced 1/4-inch thick

• 8 ounces green beans, trimmed and cut into 1/2-inch pieces

• 1 pound frozen or fresh (shelled) peas

• 3 ½ cups cooked beans with their cooking liquid clinging to them, such as cannellini and/or kidney beans or 2 (15- ounce) cans beans, drained but not rinsed

• 4 cups water or 2 cups water and 2 cups homemade chicken stock

• 1 (2 inch) piece Parmesan rind

• 1 (28 ounce) can whole peeled tomatoes with juice

• 1 pound pasta, such as orecchiette or medium shells

• Roughly torn fresh basil and grated Parmigiano-Reggiano for serving (optional)