Bring the ginger, sugar and 120ml of water to the boil in a small saucepan; reduce the heat and simmer for 5 minutes. Leave to cool. Strain the syrup through a fine sieve into a small jar or bowl, discard the ginger.
Pour some ginger syrup (around 10ml) into each glass and top up with ice cold Prosecco, garnish with a slice of lime or orange.
The syrup can be made up to a week ahead and stored in the fridge (covered).