Preheat the oven to 400 degrees F.
Line 2 baking sheets with parchment paper.
On a lightly floured work surface, unfold the puff pastry and roll lightly to flatten. Using a 2 1/2-inch cookie cutter, cut out pastry circles and place, evenly spaced, on the parchment.
Using a fork, generously prick (dock) the pastry circles to the edges.
Spread 1 teaspoon of the pesto on each circle, almost to the edge. Place a slice of tomato on top, and drizzle a tiny drop of olive oil over.
Bake until puffed and golden, 15 to 20 minutes.