Cream the butter and gradually add the white sugar, then the brown sugar. Beat in the egg, water and vanilla.
Sift together the flour, bicarb soda and salt and blend into the flour mixture. Cover the dough with plastic wrap and chill 2 hours.
Preheat the oven to 190 degrees C.
Using about a tablespoon of dough, enclose each mint or piece of mint. Place on a buttered and lined baking tray and top with a walnut half. Bake 10-12 minutes or until lightly browning. Cool on a cake rack.