Bring a large pot of salted water to a rolling boil over high heat. Add pasta and cook according to package directions until al dente, approximately 9–11 minutes depending on shape. Reserve 1 cup of pasta water before draining; this starchy liquid becomes your sauce thickener.
While pasta cooks, heat olive oil and butter in a large sauté pan over medium heat. Once butter foams, add diced onion and cook for 3–4 minutes until translucent, stirring occasionally to prevent browning.
Add minced garlic and red pepper flakes, sautéing for exactly 60 seconds until fragrant. The CIA teaches that timing—garlic burns in seconds and turns bitter, so watch carefully.
Whisk in pumpkin puree and vegetable broth, stirring constantly for 2–3 minutes to break up any lumps. The mixture should become smooth and consistent, with no visible pumpkin chunks remaining in the sauce.
Pour in heavy cream and add nutmeg, salt, and black pepper. Simmer over medium-low heat for 4–5 minutes, stirring occasionally until the sauce thickens slightly and coats the back of a spoon.
Add cooked pasta directly to the pan with the savory pumpkin pasta sauce, tossing continuously for 1–2 minutes. If the sauce seems too thick, add reserved pasta water 1/4 cup at a time until reaching desired consistency.
Remove from heat and stir in grated parmesan cheese and fresh sage. Taste and adjust seasoning with additional salt and pepper as needed before serving immediately.