Preheat oven to 375ºF. Bring a large pot of generously salted water to a boil. Once boiling, add pasta and cook until 2 minutes SHY of al dente. (The pasta should still be firm, though tender enough to bite through.) Drain the pasta into a strainer and set aside.
Meanwhile, melt butter in a large sauté pan over medium heat. Once hot, add the walnuts and 1 Tbsp. sage; cook 5 minutes, until the walnuts are toasted and aromatic. Season with a pinch of salt, and transfer mixture to a bowl.
Place pan back on the burner to medium heat. Add olive oil, along with mushrooms and onion. Cook until soft, about 8 minutes.
Stir in tomato paste, garlic, and red pepper flakes. Cook 3 to 4 minutes, until the tomato paste begins to caramelize and turn brick red. Gradually add spinach, stirring continuously until greens wilt down. Stir in oregano, salt, pepper, nutmeg, and remaining 2 tsp. fresh sage.
Add vegetable broth, stirring to release any browned bits stuck to the bottom of the pan. Stir in pumpkin puree, Parmesan, and 1/2 cup fontina cheese; continue stirring until the fontina melts and the sauce is smooth. Add pasta and stir until all noodles are well-coated in sauce.
Transfer mixture to a 13x9-inch greased baking dish. Sprinkle remaining fontina cheese overtop, along with buttery walnut-sage mixture. Cover with foil and bake for 15 minutes at 375ºF. Uncover and continue baking 10 more minutes, until cheese is completely melted and golden.