The day before making this dish, make sure to soak the beans. Add the water and the beans into a large bowl and let the beans absorb the water overnight. This will drastically cut down the cooking time.
The next day, chop up the vegetables and then you can begin to make the soup.
In a large dutch oven, add the lard or oil over medium heat and add the garlic. Cook for a minute and then add the onion and carrot. Season with salt. Add the rosemary. Sweat those vegetables slowly for 10-15 minutes. You don’t want to see any color develop. Once everything is soft and the onions are translucent, add the beans and the water they were soaking in. There should be plenty of water and if the beans and vegetables come up halfway up the pot, I’m gonna look for at least an equal amount of water, so fill the pot up with water if you need to. Bring it up to a boil then drop to a simmer. Skim off any foam as it rises to the top. Should take 40 minutes to an hour to cook the beans to al dente. Just check them like pasta. Once they are al dente, adjust the seasoning and get out a blender. Strain out about 1/2 to 2/3 of the beans and vegetables and add to the blender. Then add enough water to puree the beans smoothly. Then add that back to the pot. I like to reserve some extra beans to puree just in case I feel the soup is too thin. If the consistency looks right, bring the soup back up to a simmer, check for seasoning again, and then add the ditalini pasta. Cook that for about 10-12 minutes or until al dente, stirring the bottom of the pot constantly! This is key. The soup will begin the thicken quickly when you add the pasta and as a result, the soup is very vulnerable to the bottom scorching if you walk away. So just stay over the pot, make sure nothing sticks. The soup should be thick, the pasta should be al dente and everything should taste well seasoning. Serve immediately with some olive oil, fresh cracked black pepper and Parmigiano on top.