In a large skillet, melt the butter over medium heat. Add the mushrooms, garlic and shallots. Cook, stirring frequently, until the mushrooms are tender, about 10 minutes. Add the broth and bring to a boil. Reduce the heat and simmer until the liquid is reduced to about 1/2 cup, about 12 minutes. Stir in the cream and simmer until the sauce is thickened, 6 to 8 minutes. Stir in the thyme, 1/2 teaspoon salt and 1/2 teaspoon pepper. Set aside and keep warm.
Sprinkle the steaks evenly with salt and pepper.
In a large skillet, heat the oil over medium-high heat. Add the steaks, in batches if necessary, and cook for 4 to 5 minutes per side or until desired degree of doneness. Remove from the skillet and let stand for 10 minutes.
Serve the steaks with the mushroom sauce. Garnish with thyme leaves if desired.
You can make this sauce ahead and rewarm just before serving. For the steaks, let stand at room temperature for 30 minutes before cooking. And don't be tempted to cut into them right away after they're cooked. Let them stand for 10 minutes before serving.