Preheat the Oven: Preheat your oven to 400°F (200°C).
Season the Medallions: Pat the medallions dry with paper towels. Generously season both sides with salt and freshly ground black pepper.
Heat the Skillet: Place a cast-iron skillet or a heavy-bottomed oven-safe skillet over medium-high heat. Add the olive oil and let it heat until shimmering.
Sear the Medallions: Add the medallions to the hot skillet. Sear for 2-3 minutes on each side until a brown crust forms. Avoid moving the medallions too much to ensure a good sear.
Add Butter and Herbs: Lower the heat to medium and add the butter, smashed garlic cloves, thyme, and rosemary to the skillet. Tilt the skillet slightly and use a spoon to baste the medallions with the melted butter and herb mixture for about 1 minute.
Transfer to Oven: Transfer the skillet to the preheated oven. Alternatively, you can transfer the medallions to a baking sheet if your skillet is not oven-safe.
Cook to Desired Doneness: Cook the medallions in the oven until they reach the desired internal temperature:Medium-rare: 130°F (54°C)Medium: 140°F (60°C)Medium-well: 150°F (66°C) Rest the Meat: Remove the medallions from the oven and transfer them to a cutting board. Tent with aluminum foil and let them rest for 5 minutes to allow the juices to redistribute.
Serve: Serve the filet medallions with your favorite sides, such as roasted vegetables, mashed potatoes, or a fresh salad.