Preheat oven to 400°. Line a rimmed baking sheet with parchment paper.
Let puff pastry thaw slightly but still remain firm. Using a sharp knife, cut 1 puff pastry sheet into 9 (2¾×2¼-inch) rectangles. Place puff pastry rectangles on prepared baking sheet.
Using point of a sharp knife, cut 27 leaf shapes from remaining puff pastry sheet.
In a small bowl, whisk together egg and water. Brush egg mixture over puff pastry rectangles. Arrange 3 leaves atop each rectangle. Brush leaves with remaining egg wash.
Bake until puff pastry is puffed and deep golden brown, 13 to 15 minutes.
In a small bowl, whisk together olive oil and vinegar.
Using a sharp knife, carefully cut puff pastry rectangles in half horizontally. Spread Mushroom-Dijon Aïoli onto each cut surface of puff pastry rectangles. On bottom half of each rectangle, arrange a roast beef slice, folding to fit. Top each with a prosciutto slice and arugula, and drizzle with olive oil mixture. Cover each with a decorative puff pastry half, aïoli side down. Serve immediately.
Recipe by TeaTime Magazine at https://teatimemagazine.com/beef-wellington-stacks-recipe/