Clean, wash and cut the rhubarb into pieces of about 3 cm. Bring to the boil with 5 tablespoons of water and simmer for 5-6 minutes at low heat, stirring continuously. Sweeten with 3 tablespoons sugar and vanilla sugar. Stir starch and 2 tablespoons of water until smooth.
Stir into the boiling rhubarb and continue to cook for 2-3 minutes while stirring. Leave to cool.
Preheat oven (electric cooker: 200°C/circulating air: 175°C/gas: level 3). Roll out the puff pastry and cut into 4 squares (approx. 10 x 10 cm). Rinse 4 hollows of a muffin baking tray or ovenproof tins with cold water.
Place the dough in the hollows and prick the base several times with a fork. Bake in a hot oven for about 10 minutes.
Let the puff pastry shells cool for about 5 minutes, then carefully remove them from the trays. Sweeten the compote if necessary and distribute in the bowls. Serve with 1 scoop of ice cream each.