Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 1/4 cup sugar, ground ginger, and salt, stirring with a whisk.
Place butter in a medium bowl; beat with a mixer at medium speed until smooth (about 1 minute). Add flour mixture; beat at low speed just until combined. Add ice water; stir just until combined. Press mixture gently into a 4-inch circle on plastic wrap, and cover with additional plastic wrap. Chill for 20 minutes.
Preheat oven to 350°.
Slightly overlap 2 sheets of plastic wrap on a slightly damp surface. Unwrap and place chilled dough on plastic wrap. Cover dough with 2 additional sheets of overlapping plastic wrap. Roll dough, still covered, into an 8-inch circle (the edges of the circle will crack slightly). Remove top sheets of plastic wrap, and fit dough, plastic wrap side up, onto a baking sheet coated with cooking spray. Remove the remaining plastic wrap.
Sprinkle dough with 1 tablespoon of coarse sugar; press gently to help sugar adhere to dough. Lightly score dough into 16 wedges, cutting into, but not through, dough. Place 1 piece of crystallized ginger in each wedge; press gently to adhere.
Bake at 350° for 25 minutes or until lightly gold in color. Remove from oven; cool 5 minutes. Cut through score lines to make 16 wedges. Place on a wire rack; cool completely.