Instructions:

Begin by heating a large skillet over medium-low heat. Add equal parts unsalted butter and olive oil to the pan. Once the butter has melted, add the thinly sliced onions, stirring to coat them in the fat.

Cook the onions slowly for 30-60 minutes, stirring occasionally. The goal is to caramelize them until they're golden brown and sweet. If the onions begin to stick to the pan, deglaze with a splash of sherry, vinegar, or wine, scraping up any bits.

Season the caramelized onions with salt and black pepper to taste. If you'd like, add optional ingredients like thyme or garlic to infuse additional flavor. Once done, remove the onions from the heat and let them cool slightly.

To assemble the sandwiches, spread one slice of bread with whole grain mustard or fig jam. Layer on a generous portion of the caramelized onions, followed by a slice (or two) of Gruyère cheese. Top with another slice of bread.

Heat a clean skillet over medium-low heat and add a little more butter and olive oil. Place the assembled sandwiches in the skillet and toast until the bread is golden brown, about 3-4 minutes.

Carefully flip the sandwiches and continue to cook on the other side until the cheese is melted and the bread is crispy, about another 3-4 minutes. For an extra crispy crust, increase the heat slightly for the final minute of cooking.

Serve the onion grilled cheese sandwiches hot, optionally alongside a bowl of tomato soup for dipping.

For best results, take your time with the caramelization of the onions; patience is key to achieving that sweet flavor. Feel free to experiment with different cheese and bread combinations to suit your taste.

If you'd like a vegan version, consider using plant-based cheese and a vegan butter substitute, and add soy sauce to the onions for a savory kick. Enjoy your delicious creation!