Preheat the oven to 400°F (200°C). Arrange the smoked duck breast slices in a rosette pattern in 4 tartlet pans, alternating with the apple slices.

Cut 4 rounds of puff pastry about 1/2 inch (1 cm) larger than the pans. Prick them with a fork and cover the tartlets, tucking the edges of the pastry between the filling and the pan. Bake for 20 minutes. Let rest for 5 minutes before unmolding.