Start by slicing the yellow onions thinly. Heat a skillet over low heat and add olive oil and butter. Sauté the onions for 30-45 minutes, stirring occasionally, until they become golden brown and caramelized.

To enhance the flavor, add brown sugar and balsamic vinegar to the skillet with the onions. Cook for an additional 2-3 minutes until the mixture is beautifully glazed.

In the same skillet, increase the heat to high and add a splash of olive oil. Sauté the sliced cremini mushrooms for about 8-10 minutes until browned and tender.

Reduce the heat to medium and stir in minced garlic and fresh thyme. Cook for an additional minute until fragrant.

Pour in white wine to deglaze the skillet, scraping up any browned bits. Let the mixture simmer until it reduces slightly. Season with salt and pepper to taste.

Butter one side of each slice of sourdough bread. On the unbuttered side of two slices, spread a layer of Dijon mustard, then layer with Swiss cheese, caramelized onions, and sautéed mushrooms.

Heat the same skillet over medium-low heat and place the sandwiches inside. Cook for about 3-5 minutes on each side until golden brown.

Once grilled, remove the sandwiches and cut each in half diagonally. Serve immediately.