Bring a large pot of water to a boil over high heat.

While water is heating, set a large Dutch oven over medium heat. Add sausage and use a wooden spoon to break up. Cook, stirring frequently, until ground sausage begins to brown and crisp—about 8 minutes. Add garlic and beans, stirring often, until they too begin to crisp up—3 minutes more.

When water is boiling, stir in greens and cook 1 minute. Using a slotted spoon, transfer greens to a small bowl. Using the same cooking liquid, season water with salt and add pasta. Cook, stirring to prevent pasta from sticking, 3 minutes less than the package instructions. Reserve 1 cup pasta water before draining.

While pasta is cooking, deglaze sausage and beans with wine, scraping up any bits that have stuck to the bottom of the pan. Bring to a simmer and allow wine to evaporate over medium low heat, stirring every so often, until pasta is finished.

Reduce heat on Dutch oven to low and add ½ cup reserved pasta water. Gently fold in cooked pasta, blanched greens and butter, 1 tablespoon at a time—allowing each to melt before adding the next—tossing continuously to beautifully unify pasta and sauce. Gradually add the remaining pasta water, continuing to toss as sauce thickens. Fold in half the parmigiano. Serve in shallow bowls topped with breadcrumbs and remaining parmigiano. Waste no time eating—pasta is best enjoyed straight away.