In a large bowl beat the brown sugar, butter and shortening with an electric mixer until fluffy (do not over-beat, it will add too much air). Add the egg, honey and rosewater and beat until blended. Stir in the flour mixture with a wooden spoon, mixing until just until blended. Cover and refrigerate 1 hour.
03Preheat oven to 350 degrees F. Lightly spray 2 cookie sheets with nonstick cooking spray. Spoon the turbinado sugar in thick layer onto small plate. Using wet hands, form dough into 1 1/4-inch balls; roll in sugar to coat completely. Place balls on prepared sheets, spacing 2 to 3 inches apart.
04Bake cookies until cracked on top but still soft to touch, about 11 to 13 minutes. Cool on sheets 1 minute. Carefully transfer cookies to wire racks; cool completely.