Grate the rind from half the orange using a fine grater and set aside, then remove the skin and pith. Divide the orange into segments by cutting between the membranes, working over a bowl to catch the juice.
Whip the cream and orange rind with a hand-held electric whisk until it forms soft peaks, then add 2 tablespoons of the orange juice and the ginger syrup. Stir in the chopped ginger.
Divide the cream mixture between the brandy snap baskets, then top with the orange segments. Serve immediately.