Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. Reserve ½ cup of pasta water and then drain the pasta in a colander.
In a skillet or saucepan, heat the olive oil over medium heat. Add the diced onion and sauté for 5-7 minutes until translucent.
Add the minced garlic to the skillet and sauté for an additional minute until fragrant.
Stir in the pumpkin puree, heavy cream, vegetable broth, dried sage, and dried thyme. Mix well and bring to a simmer. Season with salt and pepper to taste.
Once the sauce is heated through and slightly thickened, add the cooked pasta to the skillet. Toss to coat the pasta evenly with the sauce. If the sauce is too thick, add some reserved pasta water to reach your desired consistency.
Stir in the grated Parmesan cheese until well combined. Adjust seasoning with more salt and pepper, if needed.
Serve the pumpkin pasta warm, garnished with extra Parmesan cheese and fresh parsley, if desired.