Heat oven to 400°F. Set up the fondue pot stand in the Jack-O-Lantern.
Cut top end off of the garlic bulb, exposing the tops of the cloves. Place on a piece of foil, drizzle with EVOO and season with salt and pepper. Wrap garlic up in the foil and roast 45-50 minutes. Let cool then squish out the garlic cloves from the skins into a food processor.
While garlic is roasting, peel and chop pumpkin into 1/2-inch cubes. Place on a large baking sheet, dress lightly with EVOO and season with salt and pepper. Roast to golden at edges and very tender, about 35 minutes.
Place pumpkin into the food processor along with the roasted garlic and purée until smooth. You should have about 2 cups worth or a bit more.
In a medium saucepot, bring the stock to a simmer over medium-high heat with the cumin, sweet smoked paprika, mustard, cayenne and nutmeg. While stock is coming up to a simmer, mix the cornstarch with the apple brandy in a small bowl until combined and almost paste-like.
In a slow and steady stream, add the cornstarch into the stock while whisking. Cook to thicken slightly, about 2-3 minutes. Add the garlic and pumpkin purée to the stock and whisk until combined.
Gradually add both cheeses to the pot while stirring in a zig-zag pattern. Cook until cheese is melted and smooth, about 5-8 minutes.
Transfer to the fondue pot and sprinkle the top with pumpkin seeds. Place pot on the stand inside the Jack-O-Lantern and serve with your favorite dippers alongside.