Take the filet mignon steaks out of the refrigerator about 30 minutes before cooking to bring them to room temperature. Season both sides generously with salt and freshly ground black pepper.

In a large skillet over medium heat, add 2 tablespoons of olive oil and 1 tablespoon of butter. Once hot, add the sliced onions. Cook, stirring occasionally, until the onions are golden brown and caramelized, about 15-20 minutes. Add the fresh thyme leaves during the last 5 minutes of cooking. Once caramelized, remove from the skillet and set aside.

In the same skillet, increase the heat to high. Add the remaining tablespoon of butter. Once melted and bubbling, add the filet mignon steaks. Sear for 3-4 minutes on each side for medium-rare, or until desired doneness. Remove the steaks from the skillet and let them rest for 5 minutes.

In the same skillet, add the chopped rehydrated porcini mushrooms and cook for 2-3 minutes. Pour in the red wine, scraping up any brown bits from the bottom of the skillet. Allow the wine to reduce by half. Next, add the beef stock and balsamic vinegar. Simmer until the sauce thickens slightly, about 5-7 minutes.

On each plate, place a seared filet mignon. Top with a generous spoonful of caramelized onions and drizzle with the porcini mushroom jus. Garnish with fresh thyme sprigs.

Serve the dish warm with your choice of sides, such as mashed potatoes or sautéed vegetables.