Chill cheese and prepare baking sheets: Place Brie in freezer until firm but not frozen, about 30 minutes. Line 2 baking sheets with parchment paper.
Preheat oven: Preheat oven to 400°F with racks in top third and middle positions.
Prepare Brie: Cut rind from Brie; discard rind. Cut Brie into ¼-inch-thick pieces.
Prepare puff pastry sheets: Place 1 puff pastry sheet on each prepared baking sheet. Using a small knife, create a border on each pastry sheet by scoring ½ inch from edges. Fold edges in on score line. (If needed, brush edges with water to help secure them.) Prick inside of pastries all over with a fork.
Add Brie and pear slices to puff pastry: Evenly distribute Brie pieces between pastries. Arrange pear slices over Brie. Sprinkle with rosemary and pepper. Drizzle with olive oil.
Bake tarts: Place 1 baking sheet on each rack in preheated oven; bake until pastries are golden and cheese is bubbly, about 20 minutes, rotating sheets between top and bottom racks halfway through baking time. Remove from oven; sprinkle with sea salt. Cool 10 minutes. Sprinkle with additional rosemary; cut each pastry into 8 pieces.
