1Add 1 1/2 tbsp butter and olive oil to a skillet and heat over MED-LOW heat. Add diced onions, salt, pepper, fresh thyme and 1 tsp of fresh rosemary to the hot skillet and sauté, stirring often, until onions are soft and starting to brown, about 10 minutes.
2Stir brown sugar into the onions and cook another minute. Transfer onions to a plate.
3Spread one side of two pieces of bread with a little bit of butter.
4To the same skillet, add remaining butter and rosemary, and heat over MED heat. Swirl to coat the bottom of the skillet with the melted butter.
5Add both pieces of bread, butter side down, and cook until bread is golden brown and crunchy, about 2-3 minutes.
6As soon as you add the bread to the skillet, add a bit of cheese to the top of each piece of bread. Once it starts to melt a little, sprinkle a couple tablespoons of the caramelized onions over the top of one of the pieces of bread.
7When the bread is good and golden brown, sandwich the pieces of bread together and cook on LOW until cheese is fully melted.
8Transfer to a plate, repeat with remaining slices of bread and ingredients.
9Slice and enjoy!