Lay out one sheet of puff pastry, on a piece of parchment paper, and drizzle the center with the syrup, leaving a 2-inch border.
Using a pastry brush, brush the syrup so that it coats the pastry evenly.
Top the syrup with slices of brie cheese and top the brie with sliced figs.
Drizzle the figs with syrup, chopped rosemary, and sugar.
Fold the edges of the pastry up and around the entire tart. The center will remain uncovered.
Brush the edges of the pastry with the beaten egg and sprinkle with sugar.
Place on a baking tray and bake at 400℉ for about 20 minutes until the bottom is evenly browned.
Let cool on a wire rack, and if you wish, sprinkle with sugar and brûlée the top
I like to eat after they have cooled enough to eat but still warm.