When the Brie is cold, remove the rind, leaving only the creamy interior. Cut the cheese into pieces and let it soften at room temperature for about 15 minutes.
Preheat the oven to 425°F (220°C).
Using a small cookie cutter, cut about 12 hearts from the puff pastry (depending on the size of your cutter). Place on a baking sheet lined with parchment paper. Using a smaller cutter, lightly score the center of each heart to create a border. Prick the pastry with a fork to prevent excessive puffing during baking.
Brush the pastry hearts lightly with olive oil. Bake for 10 to 12 minutes, or until golden and crisp.
When baked, gently press down on the center of each heart with the back of a spoon or your fingers to create a space for the brie.
Meanwhile, in a food processor, blend the softened Brie, mustard, and a drizzle of olive oil. Add salt to taste. Process until smooth and creamy, about 4-5 minutes.
Transfer the whipped Brie mixture to a pastry bag or Ziploc bag (cut a small corner for easy application).
Fill the centers of the puff pastry hearts with the whipped Brie.
