Preheat oven to 375°F. Cut the top off the pumpkin and scrape out the seeds and stringy fibers, taking care not to remove the pumpkin flesh. You want thick, sturdy walls. Brush the inside with olive oil and season generously with salt. Set on a parchment-lined baking sheet and roast 20-30 minutes, until the inner flesh is just tender but the outer walls remain firm.
Toss the Gruyère, Fontina, and cheddar with the cornstarch until evenly coated. Set aside.
Melt the butter in a saucepan over medium-low heat. Add the smashed garlic and 6 sage leaves. Cook 1 minute until fragrant. Pour in the wine and simmer 3 minutes. Lower heat, stir in the cream, and warm until steaming. Remove from heat and steep 5 minutes.
Discard the garlic and sage, then return the liquid in the saucepan to very low heat.
Slowly whisk in the cornstarch-coated cheese one small handful at a time, letting each addition melt completely before adding more. Do not allow the sauce to boil. Once completely smooth, whisk in the nutmeg.
Pour the fondue into the warm pumpkin. Optional: Broil for 1-2 minutes until lightly golden, watching closely.
Make the crispy sage garnish if using. Melt butter in a small skillet over medium heat. Add the sage leaves and fry for 1 to 2 minutes until dark green and crisp. Transfer to a paper-towel-lined plate to drain. Then scatter the crispy sage over the fondue right before serving.
Serve the fondue warm with your favorite dippers, scooping bits of roasted pumpkin into the cheese.