Heat oven to 400°. On a lightly floured surface, roll out 1 puff pastry sheet to 10 x 10 inches. Using a 2-inch round cookie cutter, punch out 25 circles. Brush each with beaten egg. Place on a cookie sheet, evenly spaced, and bake at 400° for 12 minutes or until golden brown. Repeat with second pastry sheet. Set baked rounds aside.
Melt butter in a large sauté pan over medium heat. Add mushrooms, shallots and thyme. Cook for 15 minutes or until liquid has evaporated, stirring occasionally. Season with 1/4 tsp of the salt and 1/8 tsp of the pepper.
Meanwhile, season steak with remaining 1/4 tsp salt and remaining 1/8 tsp pepper. Heat oil in a skillet over medium-high heat. Cook steak 5 minutes per side or until internal temperature reaches 130°. Cover and let rest 10 minutes. Slice into very thin bite-size pieces.
To assemble: Place a bit of the mushroom mixture and a piece of steak on each round. Garnish with fresh thyme and a pinch of coarse salt.
