Cut the (seedless) watermelon into wedges, discard the rind. Blend the flesh in a food processor with 2 T. of pureed ginger. Add chilled club soda to thin. Taste and sweeten with honey, if needed. Serve over crushed or shaved ice.
To make pureed ginger:
Peel fresh ginger and puree in a food processor with a little water or lemon juice. Can be frozen.