Place cranberries in a small bowl. Heat orange juice in a small saucepan until warm; pour over berries and let stand 10 to 15 minutes or until cranberries are soft. Drain well, pressing berries to remove excess liquid. Discard juice; set cranberries aside.
Beat butter in a large mixing bowl with an electric mixer on medium speed for 30 seconds. Add sugar and baking powder; beat until combined. Beat in eggs and orange peel. Beat in as much flour as you can with the mixer. Stir in remaining flour with a wooden spoon. Stir in cranberries and ginger.
Divide dough into three portions. With lightly floured hands, shape each portion into a 9x2-inch log; place logs 3 inches apart on an ungreased cookie sheet. Bake in a 350 degree F oven for 25 minutes or until tops are lightly browned. Cool on pan on a wire rack for 20 minutes. Reduce oven temperature to 300 degrees F. Cut each roll diagonally into 1/2-inch-thick slices.
Place slices upright on cookie sheet, leaving 1/2 inch between slices. Bake in 300 degree F oven for 15 minutes. Transfer to wire racks and cool. Store up to 3 days in a covered container at room temperature or freeze up to 3 months in a freezer container. Makes about 40.