01 - Preheat the oven to 400°F.
02 - Pat the fillets dry with paper towels. Brush all sides with olive oil and season generously with salt and black pepper.
03 - Heat a heavy ovenproof skillet over high heat. Sear the fillets for 2 minutes per side until a brown crust develops.
04 - Add butter, thyme, and crushed garlic to the skillet. Tilt the pan and spoon the melted butter over the steaks continuously for 1 minute.
05 - Transfer the skillet to the oven and roast for 8 to 10 minutes for medium-rare (130°F internal temperature) or adjust timing for preferred doneness.
06 - Remove fillets from oven and tent loosely with foil. Let rest for 5 to 10 minutes to retain juices.
07 - In a small saucepan, sauté the shallot in a little butter over medium heat until softened. Add red wine and balsamic vinegar, simmer until reduced by half. Add beef stock and simmer until reduced again by half. Optionally, add cornstarch slurry to thicken, season with salt and pepper, then strain.
08 - Place rested fillets on warm plates and drizzle generously with red wine jus.