In a large skillet over medium heat, add 1 tablespoon of olive oil. Add the thinly sliced onion and a pinch of salt. Cook, stirring occasionally, until the onions are golden brown and caramelized, about 15-20 minutes. Stir in the fennel seeds and cook for an additional 2-3 minutes. Remove from heat and set aside.

Season both sides of the filet mignon steaks generously with salt and freshly ground black pepper. In a large skillet, heat the remaining tablespoon of olive oil over high heat. Once the oil is hot, add the filet mignon steaks and sear for about 4 minutes on each side for medium-rare, or until your desired doneness is reached. Remove the steaks from the skillet and let them rest for 5 minutes.

In the same skillet, reduce the heat to medium-low and add the butter. Once the butter has melted and started to brown, add the sage leaves, cooking until fragrant, about 1 minute. Carefully add the beef broth and balsamic vinegar, scraping up any browned bits from the bottom of the skillet. Bring to a simmer and let it reduce slightly, about 2-3 minutes.

On each plate, place a filet mignon and top with a generous amount of the caramelized onion and fennel seed mixture. Drizzle the brown butter sage jus over the steaks.

Enjoy your delicious caramelized onion and fennel seed-crusted filet mignon with your choice of sides, such as roasted vegetables or mashed potatoes.