Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper or a silicone baking mat.
Place frozen puff pastry sheet on a work surface dusted with flour. Allow to thaw for 2 to 3 minutes. Using a 1 1/2 to 2-inch round cookie or biscuit cutter, cut out 12 round pieces. Place pastry rounds on the prepared baking sheet. Using a slightly smaller round cookie or biscuit cutter, cut out inner circles in each pastry round, leaving them in place. Brush each pastry round with beaten egg.
Bake in the preheated oven until browned and puffed, 13 to 15 minutes. Allow to cool completely before filling.
Cut around the small inner circle of each pastry round and gently push it down. Fill each tartlet with lemon curd and top with a blackberry. Dust with confectioners' sugar.