Boil the rigatoni in heavily salted water until al dente. Reserve 1/2 cup of pasta water before draining.
Heat 1 tbsp olive oil in a large skillet. Add the sage leaves and fry until crispy (about 30 seconds). Remove and set aside.
In the same skillet, add the remaining oil and sauté the cubed butternut squash and garlic until tender (about 10 minutes).
Add the vegetable broth to the skillet. Use an immersion blender (or carefully transfer to a standing blender) and blend the squash mixture until completely smooth and velvety.
Stir the parmesan cheese into the warm sauce until melted. Add the drained rigatoni and toss to coat, using splashes of reserved pasta water if the sauce needs thinning.
Serve immediately, garnished with the crispy sage leaves and extra parmesan.