• Thaw frozen puff pastry according to package directions (about 45 minutes).

Prepare the Brie:

• Remove and unwrap the brie from its package, place on a plate and transfer to the freezer for 20 minutes.  Do not freeze completely.
• Slice the cold brie horizontally into 2 equal rounds and place on a cutting board with the cut sides up. 
• Spread the cranberry sauce on one half of the brie, sprinkle the other half with the thyme leaves.
• Place the brie half with the thyme leaves on top of the cranberry sauce and gently press, sandwiching the two sections together.

Roll the Puff Pastry and Wrap the Brie:

• On a flour dusted work surface, roll one sheet of puff pastry to a 12x12 inch square and using the brie package as a pattern guide, cut one circle the same size as the the package.  Cut the second circle to 6 inches.
• Measure the height of the sandwiched brie and cut the remaining section of pastry into 2 ribbon strips of dough that is 1/4-inch wider than the brie and long enough together to fit around the outside of the brie.  (See Notes) 
• Flip the sandwiched brie onto the center of the larger pastry round so the cranberry half will be on top.  Position the smaller pastry round on top of the brie. 
• In a small dish, whisk the egg with the milk and brush it onto the pastry ribbons.  Wrap the pastry around the brie gluing it to the side with 1/4-inch extending above.  
• Fold the bottom edge of the pastry in toward the edge of the brie and crimp it with a fork. 
• Fold the extended portion of the pastry ribbon over the top of the pastry and crimp with a fork.
• Place the wrapped brie on a parchment-lined plate and transfer to the freezer for 1 hour.

Bake the Brie:

• When the brie has been in the freezer for 45-minutes, preheat the oven to 350°F and line a small baking sheet with parchment paper.
• Remove the brie from the freezer, brush with milk and transfer to the prepared baking sheet.
• Bake for 30 minutes until golden brown.  Transfer from the oven and allow to rest for 10 minutes before serving.