Place the mushrooms, stock and 2 cups water in a pot and bring to a gentle simmer to reconstitute the mushrooms.
Heat a soup pot over medium to medium-high heat with the olive oil. Melt the butter into the oil and add the pasta pieces. Brown the pasta until nutty and very fragrant. Remove the browned pasta and reserve in an airtight container for a make-ahead meal. If you are making the soup the same night you are serving it, leave it in the pot.
Add the garlic, celery, carrots and onions to the pot, season with salt and pepper and partially cover the pan to sweat vegetables, 7 to 8 minutes. Wilt in the kale and season with a little freshly grated nutmeg.
Remove the reconstituted mushrooms from the stock with a slotted spoon. Chop the mushrooms and add to the kale and vegetables. Add all but the last few spoonfuls of the soaking liquid to the soup pot. Add the beans and bring to a simmer.
Cool and store for a make-ahead meal. To serve, simmer the pasta in the soup until al dente. Ladle the soup into shallow bowls and top with grated cheese.