Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.
Whisk egg and water together to make egg wash.
Roll out puff pastry gently to a 14-inch square. Trim corners with a knife or pizza cutter to make a circle. Spread apricot preserves over the pastry, leaving a 1-inch margin around the edge. Sprinkle cranberries and almonds over the pastry, and place Brie cheese in the center.
Brush the edges of the pastry with some of the egg wash. Fold top and bottom of pastry over the dough; trim 2 inches off each edge. Fold remaining pastry on top to cover the Brie cheese completely. Press the seams with your fingers to seal. Remove any excess apricot preserves that leaks out.
Transfer wrapped cheese, seam-side down, to baking sheet. Brush top with egg wash.
Bake in the preheated oven until top is golden brown, about 20 minutes. Let stand before serving, about 30 minutes.