Pasta and Bean Soup

This is the first recipe I tried from The Essential New York Times Cookbook.

Tom Valenti, the owner of Ouest, in New York City, is most famous for his braised veal shanks, a dish that kept his fans jockeying for reservations through the first decade of the 21st century. But Valenti is really a master of anything hearty and succulent - like this pasta and bean soup. You won't believe it doesn't have any meat other than some diced prosciutto. Even the broth is vegetable.

2 tablespoon olive oil
1/4 lb (about 113 grams) prosciuttto, cut into medium dice (double-smoked bacon can be substituted)
1 small carrot, peeled and cut into small dice
1 small Spanish onion, cut into small dice
1 stalk celery, cut into small dice
2 cloves garlic, smashed
Coarse salt and freshly ground pepper
1 heaping tablespoon tomato paste
4 cups vegetable broth
4 cups water
2 medium baking potatoes, peeled
1 cup ditalini pasta (or macaroni)
Two 14 1/2-oz (411 g) cans cannellini beans, rinsed and drained (or white navy beans)
1 tablespoon chopped rosemary
Pinch of crushed red pepper flakes
1/4 cup freshly grated Parmesan cheese, plus more for sprinkling
Extra virgin olive oil

1. Heat the olive oil in a large heavy pot over medium heat. Add the prosciutto and cook, stirring, until it begins to render its fat, about 4 minutes. Add the carrot, onion, celery, and garlic, season with salt and pepper, and cook, stirring, until the vegetables are softened but not browned, about 5 minutes. Add the tomato paste, stir to coat the other ingredients, and cook for 2 minutes. Add the broth, water, and potatoes, raise heat to high, and bring to a boil. Lower the heat and simmer until the potatoes are very soft, 30 to 35 minutes. Transfer the potatoes to a bowl and mash them.
2. Meanwhile, add the pasta to the soup. When it is nearly done, return the potatoes to the soup. (If not serving immediately, let cool, cover, and refrigerate for up to a few days or freeze for up to 1 month. Reheat before proceeding.)
3. Add the beans to the soup and cook over medium heat until warmed through, about 3 minutes. Stir in the rosemary, crushed red pepper, and Parmesan. Taste and adjust the seasoning.
4. Ladle the soup into 8 bowls. Top each with more cheese and a drizzle of extra virgin olive oil.

Serves 8.