On a clean, lightly floured surface, roll the puff pastry out to an even thickness, about a 13-to-14-inch square. Place the Brie wheel in the center of the pastry and cut the pastry into a round 4 inches wider than the cheese on all sides. Remove the cheese and brush the pastry with a thin layer of beaten egg.
Spoon the cranberry chutney into the center of the rolled pastry and spread with the back of a spoon so it is the same size as the circle traced for the Brie. Place the cheese on top of the chutney.
Working from the bottom of the circle, begin folding the pastry over the cheese. It will not cover the cheese completely; rather the pastry should just come 1 to 2 inches over the edge of the cheese. Work all the way around the cheese until all the pastry is folded, forming a neat packet around the cheese. (If the pastry is too soft at this point, place in the refrigerator for 15 minutes to firm up.)
Cut a 2-by-2-inch 'x' in the center of the exposed cheese.
Brush the folded pastry with more beaten egg and sprinkle with the bagel spice or sesame seeds if using. Transfer to a baking pan and place in the oven. Cook until golden brown, 20 to 25 minutes. Cool 10 minutes before serving. To serve, cut into wedges. Serve with crackers if desired.