1. Heat olive oil over medium heat in a large skillet or Dutch oven. Add finely chopped onion and cook until soft and translucent, about 5 to 7 minutes.
2. Stir in minced garlic and chopped fresh sage; cook for 1 minute until fragrant.
3. Add pumpkin puree and mix well; cook for 2 to 3 minutes, stirring occasionally.
4. Pour in heavy cream; stir to create a smooth sauce.
5. Add grated Parmesan cheese; continue stirring until melted and combined.
6. Season with salt, freshly ground black pepper, and red pepper flakes if using.
7. Lower heat and simmer sauce gently for 10 to 15 minutes, stirring occasionally. Add vegetable broth or reserved pasta water if sauce thickens too much.
8. Meanwhile, bring salted water to a boil and cook pasta according to package instructions until al dente.
9. Reserve 1/2 cup pasta cooking water before draining.
10. Drain pasta and add to skillet with pumpkin feta sauce; toss to coat evenly.
11. Adjust sauce consistency with reserved pasta water, one tablespoon at a time, if needed.
12. Gently fold in half of the crumbled feta cheese.
13. Melt butter in a small pan and drizzle over pasta for extra richness.
14. Serve immediately, garnished with remaining feta cheese and toasted pumpkin seeds.