Unlike most shortbread cookies, these are made with whole wheat, which gives them a nice, toasty flavor. Slideshow: More Cookie Recipes
Preheat the oven to 350°. Sift the whole-wheat flour with the ginger, baking soda and salt into a small bowl. In a medium bowl, using a hand mixer, beat the butter with the sugar and syrup at medium speed until pale yellow and fluffy, about 3 minutes. Beat in the flour mixture just until incorporated. Knead the dough a few times in the bowl and divide in half.
On a parchment paper–lined baking sheet, roll each piece of dough into a 12-inch log, about 1 inch wide. Arrange the logs on the prepared baking sheet 6 inches apart and bake for about 15 minutes, until golden; they will spread a lot. Transfer to a rack to cool until warm. On a work surface, cut the logs crosswise into 1 1/4-inch slices. Transfer the cookies to a rack to cool before serving.
The cookies can be stored in an airtight container for 3 days.
Note: Golden syrup is widely available at Whole Foods and specialty food stores.