In a food processor, combine the pancetta and garlic and process to make a smooth pestata. Heat a large Dutch oven over medium-high heat, and add the olive oil. When the oil is hot, add the pancetta pestata. Cook and stir until it renders its fat, about 5 minutes.

Meanwhile, in the same food processor, combine the carrots, celery, onion, and parsley. Process to make a slightly chunky vegetable pestata. When the pancetta is rendered, scrape the second pestata into the pot and cook, stirring occasionally, until it dries out, about 5 minutes.

Add the tomatoes, slosh out the can with water, and add that. Add the bay leaves and 4 quarts cold water. Bring to a boil and simmer rapidly, uncovered, to reduce the soup by about a quarter and concentrate the flavors, about 1 hour.

Add the lentils, cover, and cook about 15 to 20 minutes.

Add the salt and the rice, and stir. Simmer until rice is just al dente (don’t overcook—it will cook more in the soup as you are serving) and the soup is thick and flavorful. Remove bay leaves. Serve the soup with a drizzle of olive oil and a sprinkle of grated cheese.

* If you want to make this soup ahead, make it up to the point where you add the rice, then cool and refrigerate it. To serve: return the soup to a boil with a cup or so of extra water, add the rice, and cook as directed in the recipe.