Rub steak seasoning onto both sides of the steaks and generously season with salt.
Preheat a non-stick pan over medium heat. Add oil, butter, and thyme sprigs to the pan.
Cook steaks on both sides, flipping once, until the desired temperature is reached (see below in notes). Use a thermometer. Cooking time will vary based on desired temperature of the steak. Place the steak on a plate to rest for 2-3 minutes before serving.
In a pan, over medium heat, add the milk and half of the Boursin cheese. Bring to a simmer and stir until the sauce reduces in volume and starts to thicken. Once the sauce has a smooth thickened consistency remove it from the heat. Season with salt and pepper to taste.
Serve the sauce with the steak. Garnish with remaining boursin cheese and thyme. Serve with buttered dinner rolls.