Prep the Meat: Remove the steaks from the refrigerator 20 minutes before cooking to bring them to room temperature. Pat them completely dry with paper towels and season generously on all sides with salt and freshly cracked black pepper.
Sear the Steaks: Heat the olive oil and 2 tablespoons of butter in a large cast-iron skillet over medium-high heat. Once the pan is hot and the butter is foaming, add the steaks. Sear for 4 to 5 minutes per side for medium-rare, or until they reach your desired level of doneness. Remove the steaks from the skillet and transfer them to a plate to rest, tented loosely with foil.
Sauté the Garlic: Lower the skillet heat to medium. Add the remaining tablespoon of butter to the pan. Toss in the minced garlic and cook for about 1 minute, stirring constantly, just until it is highly fragrant. Be careful not to let it burn.
Build the Sauce: Pour in the beef broth, using a wooden spoon to vigorously scrape up all the browned bits (fond) stuck to the bottom of the skillet. Bring the liquid to a simmer and let it reduce by half, which should take about 3 minutes.
Thicken with Cream: Reduce the heat to low. Stir in the heavy cream and dried thyme. Let the sauce simmer gently for 3 to 4 minutes until it thickens slightly and easily coats the back of your spoon. Stir in the fresh parsley.
Combine and Serve: Slice the rested steaks if desired. Return the steaks (and any accumulated juices from the plate) back into the skillet. Spoon the warm, creamy garlic sauce over the meat and let it warm through for 1 minute. Serve immediately with roasted potatoes and vegetables.