Cook spaghetti according to package instructions until al dente, reserving 1/2 cup pasta water, then drain.
In a large skillet over medium heat, cook bacon until crispy, transfer to paper towels, and crumble when cool.
Discard excess bacon grease, leaving 1 tablespoon in the skillet, adding olive oil if needed.
Sauté mushrooms in the skillet for 5 to 7 minutes until browned.
Add minced garlic to the skillet and cook for 1 minute until fragrant.
Stir in pumpkin puree, dried thyme, smoked paprika, nutmeg, salt, and pepper.
Pour in heavy cream and Parmesan cheese, then simmer for 2 to 3 minutes to thicken the sauce.
Add cooked spaghetti to the skillet and toss with sauce, using reserved pasta water to loosen if necessary.
Serve pasta topped with crispy bacon, chopped parsley, and extra Parmesan cheese.