Thinly slice the yellow onions and heat a large skillet over low heat. Add 2 tablespoons of olive oil and 1 tablespoon of butter. Introduce the onions, stirring frequently as they cook for 30–45 minutes until golden brown and soft.

Once caramelized, sprinkle in 1 tablespoon of brown sugar and drizzle 1 tablespoon of balsamic vinegar. Cook for an additional 2-3 minutes, then remove from heat.

In the same skillet, add more olive oil if necessary and raise the heat to medium-high. Add sliced cremini mushrooms and cook for 8-10 minutes until browned and tender.

Stir in 2 minced garlic cloves and a teaspoon of fresh thyme. Pour in 1/4 cup of dry white wine, deglazing the pan and simmering until nearly evaporated.

Remove from heat, season with salt and pepper, and combine with caramelized onions.

Butter one side of each slice of sourdough bread. On the unbuttered side of two slices, spread a layer of Dijon mustard.

Layer slices of Swiss cheese, caramelized onions, and the sautéed mushrooms on one slice of bread, then top with another slice.

Return the sandwiches to the skillet and cook over medium-low heat for 3-5 minutes per side until golden brown and the cheese melts.

Remove from the skillet, cut in half, and serve immediately.