Caramelize the onions: Heat 2 tablespoons of unsalted butter in a skillet over medium heat. Add the sliced onions and stir every few minutes. After 10 minutes, add 1 teaspoon of kosher salt. Continue to cook, stirring occasionally, for an additional 30-40 minutes until the onions turn golden. If the skillet looks dry, add 1 tablespoon of water.
Prepare the sage butter: In a small bowl, combine the chopped sage with 4 tablespoons of softened butter and 1 teaspoon kosher salt. Mix well.
Assemble the sandwiches: Lay a slice of sourdough bread (non-buttered side down). Top with slices of brie, then grated cheddar, followed by a single layer of thinly sliced apples, slightly overlapping. Add ¼ cup of caramelized onions, and finish with more cheddar cheese. Place another slice of bread on top. Spread 1 tablespoon of sage butter on the outside of the top piece of bread.
Grill the sandwiches: Heat 1 tablespoon of olive oil in a skillet over medium heat. Place the sandwiches buttered side down in the skillet. Spread the remaining sage butter evenly on the top slice of bread. Cook for about 6 minutes per side, until the bread is golden brown and the cheese is melted.
Serve warm and enjoy the delicious combination of savory caramelized onions, sweet apples, and gooey melted cheese!