In a large stockpot or Dutch oven, heat the olive oil over medium-low heat.
Add the pancetta and cook, uncovered, for 20 to 30 minutes, or until the fat is rendered.
Add the carrots, onion, fennel, garlic, beans, rosemary, salt, red pepper flakes, stock, and 4 to 6 cups of water.
Bring to a boil over medium-high heat, then reduce the heat to medium and simmer for about 1 hour, uncovered, or until the beans are cooked al dente.
Add the sweet potatoes and Parmesan cheese and simmer for about 20 minutes, or until the potatoes are tender and the beans are soft.
Ladle 3 cups of the soup, both the solids and broth, into a food processor fitted with the metal blade and puree.
Return to the pot and heat through.
Season with additional salt if necessary and serve.