Place granulated sugar and butter in a bowl; beat with a mixer at medium speed until well blended (about 3 minutes). Add corn syrup, vanilla, and egg; beat 3 minutes or until well blended.
Lightly spoon cake flour and all-purpose flour into dry measuring cups; level with a knife. Combine flours, baking powder, baking soda, salt, and 1/4 teaspoon cinnamon. Add flour mixture to butter mixture; stir until just combined. Wrap in plastic wrap; chill 1 hour.
Preheat oven to 375°.
Combine turbinado sugar and 1/2 teaspoon cinnamon in a small bowl. Shape dough into 48 balls, about 1 teaspoon each. Roll balls in cinnamon-sugar mixture. Place 2 inches apart on ungreased baking sheets. Bake at 375° for 12 minutes or until golden on bottom. Cool on wire racks.
If you prefer a slightly chewier cookie, reduce baking time to 10 minutes. A sprinkling of large-grained turbinado sugar makes a pretty presentation to attract bake sale buyers.