Gather all ingredients. Preheat oven to 400°F. Line a baking sheet with parchment paper.
Stir together fig jam, hot honey, and rosemary in a small bowl.
Spread 6 teaspoonfuls of the fig mixture into 6 (3- x 2-inch) rectangles onto the parchment paper (using 1 teaspoon for each rectangle) spacing about 2 inches apart.
Shingle about 7 apple slices over each fig mixture rectangle, and place 2 Brie slices over apples.
Using your hands, lightly press out the puff pastry sheet; cut into 6 (3 ¼- x 4 ½-inch) rectangles, and prick pastry rectangles all over with a fork.
Place 1 pastry rectangle over each fig-apple-Brie rectangle, stretching gently if necessary, and press down to seal in the fruit.
Brush each pastry rectangle with egg.
Bake in preheated oven until golden brown and flaky, about 25 minutes, lightly covering with foil after 16 minutes.
Serve immediately, drizzled with more fig mixture and sprinkled with more rosemary, if desired.
