Place a large heavy-bottomed skillet over medium/high heat and melt in 2 tablespoons butter and 1 tablespoon oil. Add the chopped mushrooms and cook for 6 minutes or until softened and most of the liquid has evaporated. Add chopped onion and cook for 3 minutes, stirring constantly.
Add minced garlic, 1 tablespoon thyme, 1/4 teaspoon salt and 1/8 teaspoon black pepper. Cook, stirring constantly, for 2 minutes or until garlic is fragrant. Transfer the mushrooms to a large plate. Wipe the pan with a wet paper towel.
Season the steaks with 1 teaspoon salt and 1/4 teaspoon black pepper. Place the same skillet over medium/high heat and add 2 tablespoons butter and 1 tablespoon oil. When the butter is hot and finished foaming, add the seasoned steaks and sear 3-5 minutes per side for medium doneness (5-6 minutes for medium doneness*), flipping once. When the steaks have reached the desired doneness, transfer them to the mushroom dish.
In the same skillet over medium/high heat, add 1/2 cup of red wine and bring to a boil until reduced by half (3 minutes), scraping bottom until dissolved. Add 1 1/2 cups beef broth and boil until 2/3 cup of liquid remains in skillet (5-7 minutes). Stir in 1/2 cup cream and let it boil for 2 minutes or until it thickens slightly. Season the sauce to taste with salt and pepper to taste.
Add the steaks and mushrooms back to the skillet, and pour some of the sauce over the steaks. Once the steaks are heated through, remove from the heat and serve, garnished with fresh thyme sprigs if desired.
A note on steak cooking times: Browning time varies based on the degree of doneness and thickness required for the steak.