In a food processor, whirl butter, 1/2 cup sugar, flour, and crystallized and ground ginger together until smooth. Or, in a bowl, with an electric mixer on medium speed, beat butter and 1/2 cup sugar until smooth; stir in flour and crystallized and ground ginger until mixture is no longer crumbly and starts to come together in a ball.
Press dough evenly into two 9-inch round pans with removable rims. Press edges of dough with fork tines to make a ridge pattern. Then, with fork tines, pierce dough all over in parallel lines 1 inch apart.
Bake shortbread in a 300° oven until firm to touch and golden at edges, about 45 minutes. Sprinkle while hot with remaining 2 tablespoons sugar, then let cool 10 minutes.
Remove pan rims from warm shortbread. Cut each round into 12 wedges. Cool completely on pan bottoms on racks.
Note: Nutritional analysis is per cookie.