Plus: More Pasta Recipes and Tips
Preheat the oven to 425°. On a medium, rimmed baking sheet, toss the squash with 1 tablespoon of the olive oil. Roast for 15 minutes, tossing once, until browned and tender; season with salt.
Meanwhile, in a pot of boiling salted water, cook the rigatoni until just al dente. Drain, reserving 1 cup of the cooking water.
Heat the remaining 3 tablespoons of olive oil in a large skillet. Add the pancetta and cook over moderate heat until lightly browned, about 5 minutes. Add the shallots, sage, crushed red pepper and a generous pinch of black pepper and cook until the shallots are soft, about 4 minutes. Add the squash, rigatoni and the reserved cooking water and cook over moderate heat, tossing gently, until the sauce is thickened and the pasta is al dente, 2 to 3 minutes; season with salt. Stir in the 1/2 cup of Pecorino. Serve the pasta in deep bowls, passing extra Pecorino at the table.