In large pot of boiling salted water, cook pasta according to package directions; drain, reserving ½ cup cooking liquid.
Meanwhile, chop enough of the sage to make 2 tbsp; reserve remaining sage leaves and set aside. Heat 2 tbsp oil in large skillet set over medium heat; sauté chopped sage, red onion, shallots, chili flakes and nutmeg for 3 to 5 minutes or until softened.
Stir in vodka; cook for 1 to 2 minutes or until slightly reduced. Add pumpkin and cream; cook for 4 to 6 minutes or until thickened.
Meanwhile, heat remaining oil in small skillet over medium heat; cook reserved sage leaves for 1 to 2 minutes or until crispy. Transfer to paper towel–lined plate. Set aside.
Stir ⅓ cup grated Parmesan into pumpkin sauce; season with salt and pepper. Toss with pasta and reserved cooking liquid.
Transfer to plates; top with crispy sage leaves and remaining Parmesan.