1. Melt 1 tablespoon butter in a large skillet over medium-low heat. Add onions, and cook, stirring occasionally, 30 minutes or until dark golden brown. Stir in salt and next 3 ingredients.
2. Place 1/4 cup cheese on each of 2 bread slices. Top each evenly with half of onion mixture. Top each with 1/4 cup cheese. Top with remaining 2 bread slices.
3. Spread outside of sandwiches with softened butter. Cook in a nonstick skillet over medium heat 2 minutes on each side or until cheese melts and bread is golden brown.