On a floured surface roll out the puff pastry into a rectangle ¼ inch thick or use already rolled puff pastry. Transfer it to a parchment paper lined baking sheet and trace a border 1 inch wide with a sharp knife taking care not to cut all the way through. Then prick with a fork all over.
Spread the pesto and arrange the cheese rounds evenly on the surface of the tart. Bake at 200C/400F for 17-20 minutes until puffed up and golden around the edges and the cheese has melted.
While the tart is baking combine the sliced basil leaves, grated garlic, lemon juice, salt and olive oil in a small bowl.
Take the tart out of the oven and let it cool, then top with sliced tomatoes and drizzle with the garlic basil sauce.
Notes
For the flakiest puff pastry, let it come to room temperature to roll it out so it is easy to work with and then chill again before baking. This allows the butter layers to rise properly.