Season the filet mignon generously with salt and freshly ground black pepper on both sides. Let them sit at room temperature for 15 minutes.

Heat olive oil in a heavy skillet (preferably cast iron) over medium-high heat. Once hot, add the steaks and sear for 3-4 minutes per side for medium-rare, or until desired doneness. Add 1 tbsp butter and minced garlic during the last minute of cooking, basting the steaks with the melted butter.

Remove the steaks from the skillet and let them rest on a plate, loosely covered with foil.

In the same skillet, add the chopped shallot and sauté for 1-2 minutes until softened. Pour in the red wine to deglaze the pan, scraping up any browned bits.

Add the beef stock and fresh thyme sprig. Bring to a simmer and let the sauce reduce by half, about 8-10 minutes. Stir occasionally.

Remove the thyme sprig and whisk in the remaining 1 tbsp butter to thicken the sauce. Season with salt and pepper to taste.

Plate the rested filet mignon and drizzle with the red wine reduction sauce. Serve immediately.