Combine the beans with the rosemary, 1 garlic clove, and enough water to cover in a medium heavy saucepan; bring to a boil over medium-high heat. Reduce heat to medium-low; simmer, uncovered, for about 20 minutes. Drain and reserve the broth, if any.

Combine the beans with ¼ cup of the reserved cooking broth (or water, if there wasn't any cooking broth left) in a food processor or blender (or use an immersion blender in the pot); process until the beans are mashed, not pureed; they shouldn't be perfectly smooth.

Warm the olive oil in a large saucepan over medium-low heat. Finely chop the remaining garlic, and add it to the oil along with the red pepper flakes; sauté, about 2 minutes, being careful not to brown the garlic. Add the mixture to the mashed beans, season with salt to taste, and continue cooking and stirring, about 5 minutes longer.

Meanwhile, boil a large pot of water over high heat. Add a tablespoon of salt and the pasta; cook until the pasta is almost tender, about 7 to 10 minutes. (You want it to be slightly undercooked, because you will continue cooking it in the sauce.) Reserve ½ cup of the pasta water and drain the pasta.

Transfer the pasta to the pot with the beans and add the reserved pasta water. Raise the heat to medium; continue cooking and stirring until the sauce has a creamy consistency, about 5 minutes. Garnish each serving with parsley.