Place a rack in the center of the oven and preheat your oven to 375 (F).
Cut 2 frozen puff pastry sheets into thirds (most store-bought frozen sheets come frozen and folded in thirds already, so just cut along the folds) to get three panels. Cut each panel into four 2 1/4-inch tall and 3-inch wide rectangles. Cut each rectangle in half. You'll have 24 little rectangle pieces that will create 12 little rectangle pockets.
In a small bowl, combine 1 large egg with a splash of milk, whisking together until the egg is beaten and the milk has been incorporated into the egg. Brush 12 of the small rectangles with egg wash. If you're using popsicle sticks for serving, place a popsicle stick halfway up the press pastry and press in gently. Place a small sliver of brie on top of the egg wash and stick. Top with 1/2 teaspoon honey. Tear a couple rosemary leaves off from your sprig and sprinkle them on top of the brie and honey. Take another puff pastry rectangle and place on top of the cheese, honey, and rosemary using a fork to press the edges together by crimping them. Prick the top of the square lightly with a fork. Repeat until you have 24 pastry squares.
Place prepared bites on a parchment-lined baking sheet and brush the tops of each pastry with remaining egg wash. Sprinkle with a touch of coarse sea salt and another couple sprigs of rosemary. Bake in the preheated oven for 12 to 14 minutes, or until golden brown.
Remove from oven and allow to cool slightly before drizzling with honey and serving immediately. Bites are best served warm.