Heat the oven to Gas Mark 7, 220°C, 200°C fan. Place a baking tray in the oven to heat up.
Remove the pastry from the fridge about 10 minutes before using, then unroll and cut into 8 rectangles, 7 x 12 cm (3 x 4½in) each. Sprinkle the sugar down the centre of each rectangle, allowing a 1 cm (1½in) rim around the outside. Thinly slice the ginger and scatter over the sugared pastry.
Trim the rhubarb and cut into 9cm (4in) lengths. Arrange in rows down the centre of the pastry. Bake for 15 minutes until the pastry is risen and the rhubarb is cooked.
While still hot, brush with a little ginger syrup from the jar. Serve with ice cream.