A pressure cooker will reduce the beans' cooking time from 1 h to 18 min. A blender or food processor will be very useful to purée the beans.
Cook the dried beans either 18 min in a pressure cooker or about 1 hour in a pot. Drain the beans, set them aside and discard the liquid.
Prepare the onion and garlic. Coarsely chop the onion and mince the garlic.
Heat the butter and olive oil in a pot over medium-low heat. Sweat the onion and garlic 2-3 min, then add the sprig of rosemary and let it infuse 3-4 min, taking care not to let it burn. Add ¾ of the beans, pour in the broth, and cook 5 min over medium heat, with some stirring.
Remove the sprig of rosemary and purée the soup in a blender or by using a food-mill. Put the mixture back into the pot.
Meanwhile, cook the pasta in a pot of boiling salted water. Drain and pour the pasta into the bean-mixture. Add the remaining whole beans and warm up the soup just 2-3 min. If the soup is too thick, it may be thinned with some broth or water.
Serve into bowls, add the grated parmesan, and drizzle with extra virgin olive oil.
This soup will keep up to 5 days in the refrigerator or up to 4 months in the freezer. If freezing, don't include the pasta but instead cook and add it later when the soup is reheated.