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Preheat oven to 400°. On a lightly floured surface, unfold puff pastry. Roll out each pastry to a 10-in. square. Cut each pastry into sixteen 2-1/2-in. squares. Cut Brie into 32 pieces; place a piece of Brie in the center of each pastry square. Bring corners of pastry over Brie and pinch edges to seal.
Place 2-in. apart on a parchment paper-lined baking sheets. In a small bowl, whisk egg and water; brush over puffs.
Bake until pastries are golden brown and puffed, 20-25 minutes. Serve warm.