On a lightly floured surface, roll out the puff pastry to about ¼-inch thick. Using a 2 1/2-inch round cookie cutter, cut 12 circles from each pastry square.  Set the second set of circles aside.  Cut excess pastry into smaller shapes to bake alongside pops.

Working with the first set of pastry rounds, place 1 teaspoon of fig jam into the center of a round.  Skewer a piece of the Brie with a lollipop stick, flatten it a bit and place it in the center of the jam.  Repeat with the remaining pastry rounds in this set.

In a small bowl, whisk the egg with the water to combine.  Brush a small amount of egg wash around the edge of each pastry round.  Take a circle from the second set and stretch it slightly so that it drapes over the brie and fig.   Press down gently around the entire edge to form the pastry pop.

Use the tines of a fork to press all around the edges of the finished pastries to seal them.  Take extra care when sealing around the sticks.

 Brush each pastry pop with egg wash and garnish with a sprinkle of flaky salt.  Transfer the pops to the prepared baking sheets and bake until golden brown, 12 to 15 minutes.  Cool for 5 minutes before serving.