Preheat oven to 180ºC. Line 2 baking trays with non-stick baking paper. Use an electric beater to beat the butter and combined sugar until pale and creamy. Add the eggs, 1 at a time, beating well after each addition.

Combine bicarbonate of soda and water in a bowl. Add to the butter mixture. Sift over the flour and ginger. Fold until combined. Fold through half the sesame seeds. Roll 2 teaspoonfuls of the mixture into a ball and flatten slightly. Place the remaining sesame seeds on a plate. Press 1 side of the ball into the sesame seeds. Repeat with remaining mixture and sesame seeds.

Place the balls, sesame seed side up, on the prepared trays, about 2cm apart. Bake, swapping the trays halfway through cooking, for 15 minutes or until golden. Set aside on the trays to cool completely.