Bring a large pot of salted water to a boil over high.
Meanwhile, heat oil in a large Dutch oven over medium.
Add shallots, garlic, chiles, and ¼ teaspoon salt to saucepan, and cook, stirring often, until garlic is lightly browned in spots, about 4 minutes.
Add half of the greens, stirring constantly and allowing greens to wilt slightly before adding remaining greens, about 2 minutes. Remove from heat.
Add pasta to the pot when the water reaches a boil, and cook according to package directions for al dente.
Transfer cooked pasta and 1 cup pasta cooking liquid to Dutch oven, and cook, stirring vigorously and tossing constantly, until the sauce is thickened, glossy, and coats the noodles, about 2 minutes. (Some liquid should still pool in the bottom of the pot.)
Remove Dutch oven from heat, and add cannellini beans and remaining ¾ teaspoon salt.
Gradually stir Parmigiano-Reggiano cheese into pasta until incorporated, about 2 minutes.
Stir in lemon juice, and season with additional salt to taste.
Serve pasta with additional Parmigiano-Reggiano and a drizzle of olive oil.
