Place the pastry on a lightly floured work surface. Using the tines of a fork, prick the pastry all over. Using a 6cm round cookie cutter, cut out 16 rounds of pastry. Place the pastry rounds on the prepared baking sheet. Lay a piece of parchment paper on top of the pastry rounds. Place another baking sheet directly on top of the parchment paper to keep the pastry even while baking. Bake for 10 to 12 minutes until golden. Remove the top baking sheet and the top piece of parchment paper.
Spread 1 teaspoon of tapenade on each pastry round. Place about 1 tablespoon of cheese on top. Arrange 2 pieces of tomato on the cheese. Bake for 5 to 7 minutes until the cheese has melted. Remove from the oven and sprinkle the chopped basil on top.
Transfer the tartlets to a platter and garnish with a pinch of fleur de sel.