Cover a baking sheet with parchment paper. Trace a circle in the middle about 3 - 4 inches (8 - 10 cm) in diameter.
Once the dough is ready, turn it out onto a lightly floured countertop. Knead a few times to release the air. Use a rolling pin to roll out to a 10 inch (25 cm) by 10 inch square. Cut into 25 smaller squares, each 2 inches (5 cm) wide. You can do this by making 4 vertical cuts and 4 horizontal cuts each space 2 inches apart.
Place a piece of brie in the center of a square. Pinch the edges together to seal, and gently roll on the countertop to shape into a smooth ball. Place on the countertop seam side facing down. Repeat with the remaining squares.
Arrange 9 of the rolls around the circle that you traced in the parchment paper. Take the remaining 16 rolls, and arrange them in a second layer surrounding the first circle.
Cover lightly and let proof for 20 - 30 minutes. Preheat the oven to 350°F.
Once the wreath is done proofing, it should look puffy and when you press a finger into the dough, it should only fill halfway. Whisk together egg and milk or water, then brush the top of the wreath with egg wash.
Place in the center rack of the oven and bake for 25 - 30 minutes until golden brown and makes a hollow noise when tapped.
Remove from the oven let cool for 5 - 10 minutes. Serve warm.