Season steaks on all sides using 1 teaspoon salt and 1 teaspoon pepper. Melt 2 tablespoons butter in large skillet over medium-high heat. Add steaks. Cook for 2 to 3 minutes, until brown on all sides. Remove from pan. Set aside. Do not clean pan. Pulse mushrooms in food processor until they form a wet paste. Set aside. Melt remaining 1 tablespoon butter in skillet, used to brown steaks, over medium-high heat. Add shallot, garlic, and thyme. Sauté 2 to 3 minutes, or until mixture becomes very aromatic. Remove thyme. Add mushroom paste, remaining 1 teaspoon salt, and ¼ teaspoon pepper. Mix well. Spread mixture evenly over bottom of skillet. Cook 3 minutes, or until moisture in mixture is mostly gone. Remove pan from heat. Set aside. Preheat oven to 400°F. On floured surface, roll out sheet of pastry to a rectangle roughly 8 inches by 14 inches. Cut into two 7-inch squares. Repeat with second sheet of pastry. Place roughly 1 tablespoon of mushroom mixture on each square. Spread evenly over each square, leaving space along edges. Place a steak on top of mushroom mixture. Split remaining mushroom mixture over tops of steaks. Whisk together egg yolks and milk in small bowl. Brush pastry edges with egg mixture. Fold pastry around steaks and seal. Place on greased sheet pan. Refrigerate about 5 minutes. Remove and brush tops with remaining egg mixture. Bake for 25 to 30 minutes, or until the internal temperature reaches 125°F for medium rare. Remove from oven. Allow to rest about 10 minutes before serving. Serves 4.