Melt butter in a medium skillet until bubbling. Add apples, brown sugar, and a pinch of 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 one side of each bread slice with oil and sprinkle lightly with salt. Place oiled-side down onto a foil-lined baking sheet. Top each bread slice with cheese, and divide the apple mixture between the two slices. Broil until cheese is melted and bubbly, about 3 minutes. Serve.
Recipe adapted from: www.thedailymeal.com