Bring water, cranberries, and 1 cup sugar to a boil in a saucepan; boil for 5 minutes. Reduce heat and simmer until cranberries pop, about 2 minutes; remove from heat to cool. Pour cranberry mixture through a strainer; reserve liquid for another use.
Whisk flour, ginger, baking powder, and baking soda together in a bowl.
Beat butter and remaining 1 cup white sugar with an electric mixer in a bowl until smooth; beat in egg. Stir drained cranberries into butter mixture; stir in flour mixture until fully incorporated. Cover dough; chill in the refrigerator until moderately firm, about 30 minutes.
Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.
Roll dough out on a lightly floured surface about 1/4 inch thick; cut into circles with a round cookie cutter. Place cookies on the prepared baking sheet; sprinkle with maple sugar.
Bake in the preheated oven until light golden on the bottom, about 10 minutes; remove to cool completely on a wire rack.
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