- In a small saucepan, reduce the balsamic vinegar and sugar by half or until syrupy. Set aside.
- In a saucepan, soften the onions in the butter over low heat, without browning. Season with salt and pepper and cook until the onions are very soft, almost translucent. Purée in the blender with the broth until smooth. Adjust the seasoning. Set aside.
- Line a baking sheet with parchment paper. Roll out the puff pastry into a 51 x 13-cm (20 x 5-inch) rectangle. Cut the dough into 6 strips of 13 x 6-cm (5 x 2 ½-inch). Prick each piece with a fork and brush with the beaten egg.
- Place the dough pieces on the baking sheet. Place the fig slices overlapping, on the puff pastry pieces. Refrigerate for 30 minutes. With the rack in the middle position, preheat the oven to 200 °C (400 °F).
- Bake the tarts for about 15 minutes or until browned. Allow to cool.
- Cut the foie gras into 12 slices. To serve, place a warm tart on one side of a plate and top with two slices of foie gras. Add some greens on the side and circle each tartlet with balsamic reduction and sweet onion purée.