In a large skillet, melt 2 tablespoons butter over medium heat. Add onions and cook, stirring occasionally, for 10 minutes. Add salt and honey. Continue to cook, stirring occasionally, until well-browned and soft, about 20 minutes more. If onions stick or start to burn, add a tablespoon of water and stir. Transfer onions to a bowl and wipe out skillet.
Divide cheese and apple slices between 2 slices of the bread. Top with onions as desired and remaining slices of bread.
Place skillet back over medium heat and add 1/2 tablespoon butter. Cook 1 sandwich, turning once, until golden brown on both sides, about 5 minutes per side. Repeat with remaining 1/2 tablespoon butter and sandwich. To serve, cut sandwiches in half and drizzle with more honey, if desired.