Season beef with salt and pepper and set aside.
Unfold puff pastry and evenly brush 1 sheet with mustard, covering entire surface. Fold over and cut into 4 equal pieces. Press the pastry edges with tines of a fork to seal and cut 3 small slits halfway deep in the center of each pastry rectangle to allow steam to escape when it cooks. Set pastry rectangles on a baking sheet lined with parchment. In a small bowl whisk egg with 1 teaspoon water. Brush pastry rectangle with egg wash and bake 25 minutes, until golden and cooked through.
Brush beef with oil. Season with salt and pepper and grill until it's nicely caramelized, turning only once, approximately 3 minutes each side. Transfer beef to a sheet pan and place in the preheated oven. Roast until medium-rare, another 10 to 12 minutes. Remove beef from the oven and place on a cutting board. Let meat rest 10 minutes before slicing. To serve, place a puff pastry rectangle on each serving plate. Drizzle with Sauteed Wild Mushroom Sauce and top with beef slices.
Heat a saute pan to medium heat. Add butter and olive oil. Add garlic and thyme leaves and saute for 3 minutes. Add mushrooms, salt and pepper, saute until golden and tender, about 10 minutes. Cook in batches, if necessary, so that the mushrooms don't steam. Return all mushrooms to pan, if working in batches. Add heavy cream and mustard and simmer 5 minutes, stirring occasionally. Serve immediately.