Heat one tablespoon oil in a large frying pan over high heat.

Season meat well with salt and pepper. Sear on both sides just until a light crust has formed but center is still raw, about one minute per side. Remove from frying pan to a platter or plate.

Cut into eight pieces, as evenly as possible. Freeze for at least two and a half hours, or up to a few days.

Heat additional one tablespoon oil in a frying pan over medium heat. Add shallots and cook until translucent. Add mushrooms, thyme, and about one teaspoon salt and cook slowly until liquid is mostly evaporated.

Add in wine and cook until almost completely evaporated. Remove from heat.

If frozen overnight, allow meat to sit out at room temperature for one hour to partially defrost.

Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).

Cut each pastry sheet into six squares.

Place a spoon of mushroom mixture onto the center of each square, then a frozen meat piece. Bring up the corners of the pastry dough and pinch closed. Place seam side down on a Gefen Parchment-lined baking sheet. Brush with egg wash.

Bake for 25 minutes or until puff pastry is lightly golden and meat is perfectly medium rare.