Preheat the oven to 425 degrees F. Line a rimmed baking sheet with parchment paper.
Place the puff pastry sheet on a lightly floured work surface and roll into a 10-inch square. Place the Brie wheel in center of the pastry. Spread the chutney over the Brie; sprinkle with the raisins and almonds. Fold the dough up and over the cheese and fillings, pleating the dough to enclose like a packet or purse. Trim the dough, if needed. Flip the packet over and place on the prepared baking sheet.
Whisk together the egg and 1 teaspoon water; brush the Brie packet with the egg mixture.
Bake until golden, about 20 minutes. Remove from the oven and sprinkle with the thyme. Cool for about 3 minutes. Serve with sliced apples and baguettes.
If you can't find mango chutney, any chutney will do.