Mix the flour, nutmeg and 1 teaspoon of the cinnamon together in a bowl, then make a well in the centre. Gradually add and whisk in enough of the sparkling water to make a smooth batter thick enough to coat the back of a spoon. Leave to stand for 20 minutes.
Fill a deep-sided saucepan one-third full with oil and heat to 180–190°C (350–375°F), or until a cube of bread browns in 30 seconds. Using a pair of tongs, dip the banana pieces, in batches, into the batter, gently lower into the hot oil and cook for 30 seconds–1 minute until golden and crisp, taking care not to overcrowd the pan with too many at a time, as they will stick together and the oil temperature will drop. Remove from the pan with a slotted spoon and drain on kitchen paper.
Mix the sugars with the cinnamon, then scatter over the hot fritters to serve.