1. Heat olive oil in a heavy skillet over high heat until very hot. Sear filets until well browned on both sides, 1 to 2 minutes per side. Remove filets from the skillet, and chill in the refrigerator for at least 1 hour. Filets must be cold.

2. In the same skillet over medium heat, melt butter. Cook and stir mushrooms, shallots, and garlic until shallots are tender and translucent and mushrooms have given off their juice, 6 to 8 minutes. Stir in 2 tablespoons of red wine, scraping and dissolving any browned flavor bits from the pan. Transfer mushroom mix into a bowl, and chill in the refrigerator for about 45 minutes.

3. Place 2 pieces of puff pastry on a work surface, and top each with a chilled filet. Spread half mushroom mixture in a neat layer on top of each filet, and top each with a piece of puff pastry. Fold and pinch edges of the pastry together, sealing in the contents, and trim to make a tidy package. Cut a small slit into top of each package.

4. Pour 1 1/2 cups of red wine into a saucepan over medium heat, and simmer until wine is reduced by half, about 15 minutes. Season wine sauce to taste with salt and pepper. Meanwhile, whisk egg into milk in a bowl, and brush pastry packages with egg mixture for a browner crust, if desired. Return bundles to the refrigerator to keep cold.

5. Preheat the oven to 450 degrees F (230 degrees C). Line a baking sheet with parchment paper.

6. Place puff pastry bundles onto the prepared baking sheet, and bake in the preheated oven until pastry is golden brown and crisp and filets are desired degree of doneness (for medium-rare, about 15 minutes; an instant-read thermometer inserted into center should read 130 degrees F (54 degrees C). Serve each filet in pastry shell with spoonfuls of wine sauce on top.

Tips

You can pause after step 2 as well as after step 3 to partially make the dish ahead, and finish up later.

You can get decorative if you choose. Use trimmings or extra pastry to cut leaves or make a little bow.