Pick over the beans, discarding any that are wrinkled, along with any grit. Place in a bowl, add cold water to cover by 4 inches and soak overnight. Drain the beans, rinse well and transfer to a saucepan. Add the garlic and water to cover by 4 inches. Bring to a gentle boil over high heat, skimming off any foam that forms on the surface. Reduce the heat to medium-low and simmer for 40 minutes. Add the salt and water if needed to keep the beans submerged, and continue to cook until the beans are tender but not mushy, about 30 to 90 minutes more, depending upon the beans. Remove from the heat and let the beans cool in their cooking liquid, then drain, reserving some of the cooking liquid. Set aside. You should have about 2 1/2 cups cooked beans.

Make Soup

Heat a large soup pot over medium-high heat. Add the olive oil and the garlic and sauté until the garlic is toasted and the oil is fragrant, about 1 minute. Add the carrots, onion and celery and cook, stirring often, until the vegetables start to soften and brown, 3 to 4 minutes. Season with salt and pepper.

Add the tomatoes, bay leaf, sage, cheese rind and enough water to cover the vegetables by 2 inches and simmer, uncovered, for 30 minutes. Add 2 cups of the cooked beans and the kale and continue to simmer for 20 to 30 minutes. Season with salt and pepper.

Just before the soup is ready, bring a saucepan three-fourths full of salted water to a boil, add the pasta, stir well and cook until al dente (tender but firm to the bite), according to the package instructions. Drain well and divide among warmed soup bowls. Ladle the soup over the pasta, drizzle with olive oil, sprinkle generously with grated cheese and serve. (If you’re not serving 8 people, just dump the rest of the pasta into the soup pot; some of the broth will get soaked up as the soup rests in your fridge. Not to worry: add a bit more water to thin it out as needed.)