Prepare the Filet Mignon: Remove the steaks from the refrigerator at least 30-60 minutes before cooking to allow them to come to room temperature. This ensures even cooking. Pat the steaks completely dry with paper towels. This is crucial for achieving a good sear. Season both sides generously with salt and freshly ground black pepper.

Sear the Steaks: Heat 15ml (1 tbsp) of olive oil and 15g (1 tbsp) of butter in a heavy-bottomed skillet (cast iron or stainless steel is ideal) over medium-high heat until the butter is melted and foaming, and the oil is shimmering. Carefully place the seasoned steaks into the hot skillet. Sear for 3-4 minutes per side for medium-rare, or until a deep brown crust forms. Adjust time based on steak thickness and desired doneness.

Baste the Steaks: Reduce the heat to medium. Add the remaining 15g (1 tbsp) of butter, smashed garlic cloves, and fresh thyme sprigs to the skillet. As the butter melts, tilt the skillet and use a spoon to continuously baste the steaks with the melted butter and aromatics for about 1-2 minutes. This adds flavor and helps cook the steaks evenly.

Check Doneness and Rest: Use an instant-read thermometer to check the internal temperature: 52°C (125°F) for rare, 57°C (135°F) for medium-rare, 63°C (145°F) for medium. Once desired temperature is reached, immediately remove the steaks from the skillet and place them on a clean cutting board or plate. Tent loosely with foil and let them rest for at least 10 minutes. Resting allows the juices to redistribute throughout the meat, resulting in a more tender and flavorful steak.

Start the Red Wine Sauce: While the steaks are resting, pour off any excess fat from the skillet, leaving behind the flavorful browned bits (fond). Return the skillet to medium heat. Add the finely minced shallot and sauté for 2-3 minutes until softened and translucent.

Deglaze the Pan: Pour in the dry red wine and scrape the bottom of the skillet with a wooden spoon to loosen all the browned bits. Let the wine simmer and reduce by about half, which should take approximately 3-5 minutes. This concentrates the flavor and cooks off the alcohol.

Build the Sauce Base: Add the beef broth and balsamic vinegar to the skillet. Bring the mixture to a simmer and let it cook for about 5-7 minutes, allowing the sauce to reduce slightly and the flavors to meld.

Thicken the Sauce: Whisk the cornstarch slurry into the simmering sauce. Continue to whisk and cook for another 1-2 minutes, until the sauce thickens to a gravy-like consistency. If the sauce becomes too thick, you can add a splash more beef broth or water. Taste and adjust seasoning with salt and pepper if needed.

Serve: Slice the rested filet mignon steaks against the grain, if desired, or serve whole. Plate the steaks and generously spoon the warm red wine sauce over the top. Serve immediately with your favorite side dishes, such as mashed potatoes, roasted asparagus, or a simple green salad.