Melt 2 tablespoons butter with 1 tablespoon oil in heavy large skillet over medium heat. Add mushrooms and saute until tender, about 10 minutes. Add 1/4 cup shallots and half of 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 tablespoon butter with 1 tablespoon 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 plate.
Add remaining 1/4 cup shallots and garlic to same skillet. Saute 2 minutes. Add Madeira and boil until reduced by half, about 3 minutes. Add broth and boil until mixture is reduced to 2/3 cup, about 6 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 to skillet and cook until heated through, about 1 minute. Transfer to plates. Spoon sauce over and serve.