Melt the butter in a medium skillet over medium heat. Add the sliced apples and cook, stirring often, for 5 to 7 minutes, or until golden and just beginning to brown at the edges. Drizzle the maple syrup over the apples and continue cooking, stirring, for 2 to 3 minutes more, until the syrup forms a light glaze on the apple slices. Stir in the sage, season with salt and pepper, and remove from the heat.

Preheat a large griddle or skillet over medium heat. Butter one side of each slice of bread. Place a slice buttered-side down on the griddle, then layer with ⅛ of the shredded cheese, ¼ of the maple sage apples, and another ⅛ of the cheese. Top with a second slice of bread, buttered-side up. Repeat to build 4 sandwiches.

Cook the sandwiches for 3 to 5 minutes per side, until the bread is golden brown and the cheese has melted (timing will vary depending on your griddle or stovetop, so keep an eye on them). Transfer to a cutting board, cut in half, and serve warm.