Preheat the oven to 220°C and line a large baking tray with baking paper.
Cut the Chantenay carrots into quarters and steam them briefly.
Unroll the pastry on a baking sheet and cut out the shapes. Use a fork to make some holes in the dough. Bake the pastry in the oven for about 12-15 minutes until puffed up and they are golden brown. How long this takes depends on your oven.
Remove the pastry from the oven and add some tomato pesto. Add carrots, sliced goat cheese, olive oil and pepper and salt to taste.
Place the tarts into the oven again and bake for about 5-7 minutes until the cheese has melted and the Chantenay carrots are hot. Remove them from the oven, sprinkle with some chopped chives and they are ready!