One day ahead: Combine the cannellini beans and 4 cups of water in a large pot that has a tight-fitting lid. Soak the beans for 24 hours.
The day of serving: Preheat the oven to 350 degrees F.
Drain the beans. In a Dutch oven or heavy bottomed pot, combine the beans, onion, carrot, celery, salt, and 16 cups of water. Bring to a boil, reduce the heat to a simmer, cover, and cook until fully cooked and creamy, 4 to 4 1/2 hours. Let cool.
While the beans are cooking, combine the garlic, olive oil, rosemary, and chile in a medium saucepan over medium heat. When the oil begins to bubble, reduce the heat to low and cook the garlic in the oil until the cloves are soft and tender, 30 to 45 minutes; be careful not to brown the garlic. Remove from the heat, leave in the pan, and let cool.
Strain the cannellini beans, reserving the cooking liquid, and add the beans back to the Dutch oven. Add the garlic-olive oil mixture to the beans and stir to incorporate. Bring to a simmer over medium heat and then turn down to low and cook together for 10 minutes, stirring frequently to incorporate the ingredients into the beans. Set aside. Remove the rosemary sprigs and chile pod and discard.
In a small saute pan over medium heat, cook the pancetta until tender but not crispy, 4 to 5 minutes. Remove from the heat and set aside.
Working in small batches, use a blender to puree the bean mixture by adding a small amount (about 1/4 cup) of the reserved bean cooking liquid to the beans in the blender and pureeing to a smooth, pourable soup consistency. Repeat with the entire bean mixture.
To serve: Warm the soup over medium heat, carefully stirring in more cooking liquid from the beans if the soup thickens while warming. Ladle about 1 cup of soup in each bowl; divide the ditalini between the 4 servings, placing it in a small pile in the center of the soup. Sprinkle the pancetta over each pile of the ditalini, drizzle a little of the olive oil over the top and finish with a little freshly cracked black pepper. Serve immediately.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.