Melt 2 Tbsp butter with 1 Tbsp oil in a heavy large skillet over medium heat. Add mushrooms and sauté until tender, about 10 minutes. Add 1/4 cup shallots and half the garlic and sauté until shallots are soft, about 3 minutes. Stir in thyme; season with salt and pepper. Transfer mushroom mixture to medium bowl.
Melt remaining 1 Tbsp butter with 1 Tbsp oil in same skillet over medium-high heat. Sprinkle steaks with salt and pepper. Add to skillet and cook to desired doneness, about 3 minutes per side for medium-rare. Transfer steaks to a plate.
Add remaining 1/4 cup shallots and garlic to same skillet. Sauté 2 minutes. Add Madeira and boil until mixture is reduced to 1/3 cup, about 6 minutes. Add Beef broth and boil about 3 minutes. Add cream and boil until sauce thickens slightly, about 2 minutes. Stir in mushroom mixture. Season sauce to taste with salt and pepper.
Return steaks and any juices to skillet and cook until heated through, about 1 minute. Transfer to plates. Spoon sauce over and serve.
Recipe Notes
I went basic with this. Served with asparagus and white wine. Yes, I prefer white wine with this!