Line a baking sheet with parchment paper.
Cut the peaches in half, remove the stones, then slice them into thin, half-moon shapes.
Mix together the frangipane cream.
Unroll the pastry. Using a pizza-cutter, cut the pastry into approx. 8x5 cm rectangles (the peach pieces should fit nicely across them). Put them on the baking sheet, allowing some space between them.
Using a fork, prick the base of each tartlet a few times, then spread some frangipane over them (don’t go to the edge).
Arrange the peach slices neatly on the top, slightly overlapping each other.
Heat the jam with 1-2 Tbsp of water and brush the top of the peach slices with this mixture.
Rest the sheet in the fridge for 15 minutes.
Turn on your oven to 200°C.
Take the tarts out of the fridge and bake them for 12- 15 minutes (in the middle of the oven), until golden brown.
Let them cool on a wire-rack.
Dust them with icing sugar just before serving.