Preheat the oven to 425 degrees F and line 2 baking sheets with parchment paper.
Whisk together the egg with 1 tablespoon of water in a small bowl for an egg wash. Cut the side rind off the Brie, then cut the Brie into 32 even pieces. Set aside.
Unfold a puff pastry sheet on a lightly floured surface. Roll out into a 13-inch square. Cut into 16 squares. Repeat with the second sheet so you have 32 squares total.
Top a pastry square with about 1/2 teaspoon cranberry sauce, 1/4 teaspoon walnuts, a piece of Brie and a pinch of thyme.
Use your finger or a pastry brush to brush the edges of the pastry square with egg wash until lightly coated and tacky. Pinch 2 opposite points together, then pinch the remaining 2 points together so that you have a little package. Repeat with the remaining pastry squares and filling.
Transfer the pouches to the prepared baking sheets and brush with the remaining egg wash. Bake until puffed and golden brown, 15 to 20 minutes.
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