This melt is inspired by a Cheddar-apple pie, a genius and savory twist on everyone's favorite all-American dessert. This recipe keeps the apples sweet but gives them a savory edge with sharp Cheddar and tarragon for a hint of licorice. Make sure to choose an apple that will hold its shape, and strike a balance between tart and sweet.
Preheat the broiler.
Melt the butter in a saute pan until foamy. Add the apples, sugar, and a large pinch salt. Cook over medium-low heat, stirring frequently, until apples are softened and caramelized, 15 to 20 minutes. Stir in the wine and tarragon, raise the heat to medium, and cook until the wine has been absorbed.
Brush 1 side of each bread slice with the oil, and sprinkle lightly with salt. Place oiled-side down onto a foil-lined baking sheet. Top each bread slice with a slice of cheese, and divide the apple mixture between 2 slices. Broil until the cheese is melted and bubbly, about 3 minutes. Assemble and serve.