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In a large bowl, cream the butter, honey, molasses, brown sugar, and egg with an electric mixer or vigorously by hand until light and smooth, scraping down the sides as needed.
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In a separate medium bowl, whisk together the white whole wheat flour, rye flour, cinnamon, ground ginger, cardamom, baking powder, and salt. Add the flour mixture to the butter/sugar mixture and mix until blended, scraping down the sides as needed. Add the crystallized ginger and mix again just to blend. Cover and refrigerate at least 30 minutes.
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When ready to bake, preheat oven to 350 degrees. Pour about 1/2 cup of sugar (coarse sugar if you have it) into a cereal-sized bowl. Make balls of dough that are about 2 teaspoons each, rolling them between the palms of your hands until smooth. Roll the balls of dough in sugar, coating them entirely. Arrange the dough on a baking sheet with 1 1/2 to 2 inches of space between. Use the bottom of a glass to gently flatten the cookies until they are about 1/3-inch thick.
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Put cookies into the oven to bake. For a chewy cookie, bake until the color begins to darken, particularly around the edges, about 10 minutes. If you cook them longer, they will be crispy.
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Remove from oven and let cool for at least 15 minutes. Transfer to a covered storage container.