Heat the olive oil in a large pan or cast iron skillet over medium heat. Once hot, add the sliced onions. Cook, stirring frequently with a wooden spoon, until the onions begin to soften, about 20 minutes.

Add the butter and continue cooking for an additional 20 minutes, stirring every 2-4 minutes. Be attentive to avoid burning the onions; adjust the heat if needed.

Mix in the salt, sugar, cinnamon, and black pepper, and cook for another 15 minutes, stirring regularly. At the 12-minute mark, add the minced garlic.

Pour in the red wine to deglaze the pan. Scrape the bottom and sides of the pan with the wooden spoon to lift any caramelized bits. Let cook for 2-3 minutes, until the wine has mostly evaporated. Set the onions aside.

Melt 4 tbsp of butter in a microwave-safe dish with a pinch of rosemary and thyme. Brush the melted butter onto one side of each slice of bread.

Place two slices of bread, butter-side-down, into the skillet. Top with the caramelized onions.

Sprinkle the shredded white cheddar on top of the onions.

Cover with the remaining slices of bread, butter-side-up. Cook on medium heat for about 5 minutes, or until the bottom is golden and crispy. Meanwhile, preheat your oven to broil.

Transfer the skillet to the oven and broil for 1-2 minutes, or until the top bread is golden and crispy.

Remove from the oven, sprinkle the Gruyère cheese on top, and return to the oven. Broil for an additional 1-2 minutes, or until the cheese is melted and bubbly.

Remove from the oven, cut the sandwiches in half, and garnish with extra rosemary and thyme. Serve hot.