Combine mushrooms, shallots, garlic thyme and a dash of fine sea salt and freshly ground pepper in a food processor. Pulse until mixture starts to become a paste.
Melt unsalted butter in a skillet over medium-high heat. Add mushroom mixture, cooking until mixture starts to soften and liquid has evaporated. Mixture should be slightly dry. Remove and allow it to cool
Dab cut pieces of beef dry. Heat extra virgin olive oil over high heat in a large skillet. Add beef and sear all sides. Do not crowd the pan, work in batches if you need to. Remove to a paper towel lined plate and allow to cool.
Cut prosciutto slices into smaller pieces, just enough to wrap each piece of beef tenderloin. On each piece, place a dab of coarse Dijon mustard and the mushroom mixture, then a piece of beef, wrap. Continue with all pieces
Preheat oven to 400 degrees and line a baking sheet with parchment paper.
Unroll defrosted puff pastry, continue to roll on a dry surface until 16x9 inches. Cut into 12 equal squares. Place a piece of rolled beef in the center of each. wrap up, securely the edges. Place each, seam down, on a parchment lined baking sheet. Continue with all pieces.
Baste tops with lightly beaten eggs. Bake for 12-14 minutes or until tops are lightly browned. Remove and allow to cool slightly before serving. Puff pastry is best served same day.
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