Take the filet mignons out of the refrigerator about 30 minutes before cooking to let them to come to room temperature. Thoroughly pat the steaks dry with paper towels and season generously on all sides with salt and freshly ground black pepper.

Place your oven-safe skillet over medium-high to high heat. Allow it to heat for 3-5 minutes, until it's very hot and just starting to smoke lightly. Add oil for a minute before carefully placing the seasoned filet mignons in the hot skillet. Sear for 3-6 minutes per side, depending on thickness and desired crust, until a deep golden-brown crust forms. Cook until the internal temperature reaches 5-10 degrees Fahrenheit below your desired doneness as per a meat thermometer (e.g., for medium-rare 130 degrees Fahrenheit, cook to 120-125 degrees Fahrenheit in the oven).

While the steaks are resting, reduce the heat under the skillet to medium-low. If there's excessive rendered fat, you can carefully pour out most of it, leaving about 1 tablespoon. Keep all the browned bits in the pan. Add the butter, and once it’s melted, add the garlic to the pan. Cook, stirring, for 1-2 minutes until softened and fragrant.

Pour in the balsamic vinegar and immediately scrape up all the browned bits from the bottom of the pan with a wooden spoon or spatula.

Add the honey or maple syrup and bring the mixture to a gentle simmer. Let it cook, stirring occasionally, for 4-7 minutes, or until the sauce has reduced significantly and begins to thicken into a syrupy glaze consistency that coats the back of a spoon. The reduction process will intensify the balsamic flavor.

Taste the sauce and adjust seasoning with salt and pepper if needed. Pour it over your steaks and enjoy!