Preheat oven to 400°. Line a rimmed baking sheet with parchment paper.
Place 1 pastry sheet on prepared pan. Spread evenly with mustard, leaving a 1-inch border around edges. Top with turkey, overlapping slices slightly; top evenly with cheese. Spread cranberry sauce over cheese. Sprinkle with arugula.
Brush edges with beaten egg; top with remaining pastry sheet. Crimp edges with a fork; brush top with egg. Cut four 1-inch vents in top.
Bake until golden brown and crisp, approximately 20 minutes. Let cool on a wire rack 5 minutes before cutting into pieces.
Recipe by Louisiana Cookin' at https://louisianacookin.com/turkey-and-brie-stuffed-pastry/