In a wide skillet large enough to accommodate the cooked pasta later, warm the olive oil over medium-low heat. Add the garlic and sausage and sauté. When the garlic is well softened and fragrant and the sausage is lightly browned, after about 7 minutes, add the beans. Using a wooden spoon, stir them with the oil and break them up a little. Stir in the bean liquid and the meat broth. Simmer, uncovered, over medium-low heat until the liquid has thickened to a sauce consistency, about 20 minutes.

Meanwhile, bring a large pot filled with water to a rolling boil. Stir in the pasta and the kosher salt. Cook, always over the highest possible heat and stirring constantly to prevent the strands from sticking together, until the pasta is almost cooked. Cooking time depends on what type of pasta is used. Fresh bigoli are cooked as soon as the water returns to the boil and the noodles rise to the surface, about 3 minutes. Factory-made bucatini cook quickly because they are hollow and their walls are thin, no more than 7 minutes. Penne or perciatelli usually take another minute or two to cook.

Add a glass of cold water to the pot to arrest the boiling and drain immediately. Transfer the pasta to the skillet with the bean sauce. Toss together over high heat with the parsley and plenty of pepper. Serve immediately.