Place oven racks in bottom third and middle of oven and preheat to 350°F; Put a pot of water for your pasta on the stove to boil.
Toss mushrooms, garlic, thyme, smoked chili flakes or red pepper flakes, 1/4 cup oil, and 1/2 teaSpoon salt on a rimmed baking sheet. Roast on bottom rack around 25 minutes, tossing halfway through until deeply golden brown and crisped. Check the oven after 15 minutes.
Cook pasta according to package. Drain, reserving 2 cups pasta water. Set aside.
In a skillet add 2 TableSpoons black sage honey brown butter. Then add the shallots and sauté until translucent. Season with a pinch of salt, and add the garlic and cook about 1 minute until fragrant.
Add pumpkin puree, mascarpone cheese and 1 cup of pasta water. If you want pasta sauce that is looser, add more pasta water until it reaches the consistency that you like.
Add the parmesan cheese. Mix to combine.
Taste and adjust salt & pepper if needed. I use smoked paprika sea salt.
Transfer cooked pici pasta to the pan and toss to combine.
Serve the pasta immediately and top with the crispy mushrooms or the crispy pancetta.