How to Make It
In a large pot of salted boiling water, cook the rigatoni until al dente, about 8 minutes. Drain, reserving 1/2 cup of the pasta water.
Meanwhile, in a large, deep skillet, melt 2 tablespoons of the butter in the olive oil. Add the scallions, leeks and shallot and season with salt and pepper. Cook over moderate heat, stirring occasionally, until softened, about 8 minutes. Stir in the sage.
Increase the heat to high. Season the livers with salt and pepper and add them to the skillet. Cook, stirring occasionally, until golden all over, about 2 minutes. Add the wine and cook until evaporated, 1 minute.
Add the pasta, 1/4 cup of the reserved pasta water, 1/2 cup of the cheese and the remaining 1 tablespoon of butter to the livers and season with salt and pepper. Remove the skillet from the heat and toss the pasta. Add the remaining pasta water if necessary. Transfer the pasta to plates, top with the remaining 1/2 cup of cheese and serve with lemon wedges.