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Makes 24 cookies
For the sorghum blend
1 1/2 cups sorghum flour, such as Bob's Red Mill brand
1 1/2 cups potato starch or cornstarch
1 cup tapioca flour
For the cookies
8 tablespoons vegan margarine, such as Earth Balance Natural Buttery Spread, at room temperature
1/2 cup sugar, plus 2 tablespoons for rolling
1/2 cup packed light brown sugar
1 large egg
2 teaspoons vanilla extract
2 cups sorghum blend (see headnote; first 3 ingredients)
1 teaspoon xanthan gum
1 1/2 teaspoons ground cinnamon
1 teaspoon ground ginger
1/2 teaspoon freshly grated nutmeg
1/2 teaspoon baking powder
1/2 teaspoon salt
1/4 tablespoon ground allspice
1/4 teaspoon ground cloves
For the frosting
1 cup confectioners' sugar
1 tablespoon water, or as needed
1 teaspoon salted vegan margarine, such as Earth Balance brand, at room temperature
1/2 teaspoon vanilla extract
For the sorghum blend: Whisk together the sorghum flour, potato starch or cornstarch and the tapioca flour in a container with a tight-fitting lid.
For the cookies: Combine the vegan margarine, 1/2 cup of the sugar and the brown sugar in the bowl of a stand mixer or hand-held electric mixer. Beat on low speed for 1 to 2 minutes, until smooth. Add the egg and vanilla extract, mixing to incorporate, then gradually add the sorghum blend, xanthan gum, cinnamon, ginger, nutmeg, baking powder, salt, allspice and cloves. Beat on low speed just until blended. Gather the dough into a ball and knead it with your hands until it is smooth. Flatten it into a disk, wrap in plastic wrap and refrigerate for 2 hours.
Position oven racks in the upper and lower thirds of the oven; preheat to 375 degrees. Line two 15-by-10-inch baking sheets (not nonstick) with parchment paper.
Spread the remaining 2 tablespoons of sugar on a plate. Use wet hands or a No. 50 metal ice cream scoop to shape the dough into 1 1/2-inch balls; roll the balls in the sugar, then place them 2 inches apart on the baking sheets. Bake for 6 to 7 minutes, then rotate the sheets top to bottom and front to back. Bake for 6 to 8 minutes, until the cookies are golden brown. Let the cookies cool on the sheets for 2 to 3 minutes, then transfer them to a wire rack to cool completely. (At this point, the unfrosted cookies can be stored in an airtight container for 2 days or can be wrapped well and frozen for up to 1 month.
For the frosting: Whisk together the confectioners' sugar, water, vegan margarine and vanilla extract in a medium bowl until very smooth. Add sugar or water as needed to achieve a spreadable consistency. Use a rounded or offset knife to spread the top of each cookie with a scant teaspoon of frosting, then transfer the cookies to a wire rack until the frosting has set.