Ingredients

3 tablespoons extra-virgin olive oil

2 leeks, white and light-green parts only, sliced 1/2 inch thick

2 carrots, sliced 1/2 inch thick

2 stalks celery, sliced 1/2 inch thick

4 sprigs thyme

2 sprigs basil

6 sprigs flat-leaf parsley

1 bay leaf

1/4 teaspoon black peppercorns

Kosher salt

2 pounds fresh fava beans (about 1 1/2 cups shelled)

1 1/2 cups frozen baby lima beans

1 can (14.5 ounces) diced tomatoes, drained

4 ounces thin spaghetti, broken into thirds

Kosher salt and freshly ground pepper

1/4 cup packed basil leaves, thinly sliced

Finely grated Parmiggiano-Reggiano, for serving

Extra-virgin olive oil, for drizzling

Preparation

Vegetable Stock:Heat oil in a large pot over medium. Add leeks, carrots, and celery; cook, stirring occasionally, until softened, about 10 minutes. Add 10 cups water, thyme, basil, parsley, bay leaf, and peppercorns. Bring to a boil, then reduce heat to a gentle simmer and cook, uncovered, 1 hour. Season with salt.

Strain stock through a fine sieve into a medium pot, pressing on solids to extract as much liquid as possible (you should have 7 cups); discard solids.

Soup:Prepare ice-water bath. Bring a large pot of salted water to a boil. Add fava beans and blanch 2 minutes. Transfer to ice-water bath; drain. Remove outer skin from fava beans.

Bring stock to a simmer over medium-high heat. Add lima beans, tomatoes, and pasta; cook, stirring occasionally, until beans are tender and pasta is al dente, about 10 minutes. Stir in fava beans; season with salt and pepper. Ladle soup into bowls; top with basil, cheese, and a drizzle of oil.

Heat oil in a large pot over medium. Add leeks, carrots, and celery; cook, stirring occasionally, until softened, about 10 minutes. Add 10 cups water, thyme, basil, parsley, bay leaf, and peppercorns. Bring to a boil, then reduce heat to a gentle simmer and cook, uncovered, 1 hour. Season with salt. Prepare ice-water bath. Bring a large pot of salted water to a boil. Add fava beans and blanch 2 minutes. Transfer to ice-water bath; drain. Remove outer skin from fava beans.