Bring a large pot of salted water to a boil and cook the spaghetti according to package directions until al dente, usually 8-10 minutes. Before draining, reserve 1/2 cup of the starchy pasta water.

While the pasta cooks, place the bacon in a large cold skillet and turn the heat to medium. Cook for 6-8 minutes, flipping occasionally, until crispy and golden brown. Transfer to paper towels to drain, then crumble once cooled.

Pour off most of the bacon grease, leaving about 1 tablespoon (it should just coat the bottom of the pan). Add olive oil if needed. Increase heat to medium-high and add the sliced mushrooms in a single layer. Cook undisturbed for 3-4 minutes until golden-brown, then stir and cook another 3 minutes.

Reduce heat to medium and add the minced garlic, stirring constantly for about 1 minute until fragrant but not browned.

Add the pumpkin puree, thyme, smoked paprika, nutmeg, salt, and pepper to the skillet. Stir everything together until well combined and heated through, about 2 minutes.

Pour in the heavy cream and grated Parmesan cheese, stirring until the cheese melts and the sauce becomes smooth and creamy. Let it simmer gently for 2-3 minutes to thicken slightly.

Add the drained spaghetti to the skillet and toss everything together using tongs, ensuring each strand gets coated in sauce. If needed, add reserved pasta water one tablespoon at a time until you reach your desired consistency.

Serve immediately topped with the crumbled bacon, fresh chopped parsley, and extra Parmesan cheese if desired.