Mom's Minestrone

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 1/2 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)

Instructions

1. Heat oil and butter in a large pot over medium-low heat (the goal is to build flavor slowly at first). When the butter has melted, add leeks and garlic and season with a pinch each of salt and pepper. Cook, stirring occasionally (and get used to this step, since you are going to be doing it every time you add a new ingredient) until they have wilted and softened, about 4 minutes.
2. Remark over how wonderful the kitchen smells, then add potatoes and a pinch each of salt and pepper. Stir to combine, and cook until the potatoes begin to sizzle. Add carrots and a pinch each of salt and pepper and stir. By now the pan will start to be crowded, so you can increase the heat to medium.
3. Repeat these steps while adding each new ingredient, seasoning, stirring and allowing to sizzle before moving on to the next, adding in this order: celery, yellow squash, zucchini, green beans and peas. It should almost look like you are making a vegetable potpie filling.
4. Add beans and the liquid clinging to them. Add a pinch each of salt and pepper. Add water (or water and stock). Increase heat to medium-high and add Parmesan rind. Cook, stirring occasionally, until the soup comes to a simmer. Add tomatoes and their juices and a pinch each of salt and pepper; bring to a gentle simmer.
5. Reduce heat to a bare simmer and cover the pot. Continue simmering, stirring occasionally, until it has thickened into a hearty stew, about 3 hours. Taste for seasoning and adjust as you see fit.
6. Just before serving, cook pasta according to package directions. Drain.
7. Serve the soup with the pasta. Top with cheese and basil and a drizzle of olive oil, if desired.