In a small bowl, mix the goat cheese and pumpkin puree until fully combined and smooth. This spread is really the heart of the sandwich, giving it that unmistakable pumpkin flavor in every bite. Stir in the minced sage right into the mixture, or sprinkle it on separately once it's spread on the bread.
Lay out all 8 slices of bread and spread a thin, even layer of softened butter on one side of each slice. Buttering evenly is key here, since it's what gives you that crisp, golden crust once the sandwich hits the pan. Keep the buttered sides facing outward when you assemble.
On the unbuttered side of 4 bread slices, spread a generous layer of the pumpkin goat cheese mixture. Top with a slice of white cheddar, a slice of orange cheddar, a few apple slices, and another slice of white cheddar. This layering order helps the cheese melt around the apple slices evenly.
Place the remaining 4 bread slices on top, buttered side facing up, to close each sandwich. Press down gently with your palm so the layers hold together nicely before they hit the skillet. This little step keeps everything from sliding around while cooking.
Heat a large non-stick skillet over medium heat and place the sandwiches inside once it's warm. Cook for 3 to 4 minutes per side, pressing gently with a spatula, until the bread turns deep golden brown and the cheese melts completely. Keep an eye on the heat since pumpkin bread browns faster than regular bread.
Remove the sandwiches from the skillet and let them rest for a minute before slicing in half. This short rest helps the cheese set slightly so it doesn't ooze out everywhere when you cut it. Serve warm while the cheese is still wonderfully melty.