Preheat oven to 350 F.
Place the pumpkin on a baking sheet cut-side down, and roast for 50-60 minutes, until tender. When cool enough to handle, scoop the pumpkin flesh into a bowl and roughly mash with a fork. Set aside.
In a small bowl, combine the salt, chili powder, and paprika. Set aside.
Spread butter onto one side of each slice of bread. Spread about 1/2 cup of the mashed pumpkin onto the unbuttered sides of 4 of the slices of bread. Sprinkle the pumpkin with the spice mixture, then with the grated cheese. Top each sandwich with the remaining slices of bread, buttered sides facing up.
Heat a large skillet over medium heat. Cook the sandwiches, in batches if needed, for about 5 minutes per side, until the cheese has melted and the bread is golden brown.