Preheat the oven to 200C/400F/Gas 6 and grease two baking sheets.
Roll out each piece of pastry on a flat surface and cut each one into 5cm/2in square pieces - ending up with about 40 squares. Place the squares on two large, greased baking sheets about 2.5cm/1in apart to allow for the pastry to puff up.
Place ½ tsp pesto in the middle of each square and place half a cherry tomato on top.
Top with a little more pesto and lay across an asparagus spear.
Sprinkle a little grated parmesan and a little olive oil over each one.
Season well and bake in the oven for 5-8 minutes or until the pastry is golden and the cheese has melted.