Preheat oven to 400°F. Place pastry on a lightly floured surface and roll out to a 12-inch square. Cut into 12 3-inch squares and place on a parchment-lined baking sheet.
Heat oil in a large skillet over medium heat. Add onion and cook, stirring occasionally, until golden brown, about 20 minutes. Add vinegar, sugar and nutmeg; cook until syrup is thickened, about 5 minutes.
Divide Brie among tartlets; top with caramelized onions. Bake until golden brown, about 15 minutes.