Preheat the oven to 425 degrees.
In a mixing bowl toss the squash with 2 tablespoons of the olive oil and salt. Spread onto a 13x18 baking sheet and roast for 20-25 minutes tossing halfway through. Transfer to a plate and set aside.
Bring a large pot of generously salted water to a boil and cook the rigatoni until al dente. Drain and reserve about a cup of cooking water. Set aside.
Put a large saute` pan over a medium-high flame and heat the remaining oil. Add the shallots and saute` for about 3-4 minutes.
Add the pancetta and sage and saute` until crisp, about 5-7 minutes.
Add in the radicchio and saute` until just wilted, about 2 minutes.
Add the chicken broth and saute` scraping up the bits from the bottom of the pan with a wooden spoon. Cook for 1-2 minutes and add in the squash and the rigatoni.
Toss the pasta with everything using some of the cooking water if it's a bit dry. Turn off the heat and add the pecorino cheese tossing to melt.
Serve in warm bowls with an extra sprinkle of pecorino!