Stir gluten-free flour, baking powder, xanthan gum, nutmeg, and salt together in a large bowl.
Beat sugar and shortening with an electric mixer in a large bowl until smooth. Add beaten eggs, milk, and vanilla extract; beat until light and airy, about 2 minutes. Add gluten-free flour mixture in small batches and stir until dough is just combined.
Pat dough into a ball, wrap in plastic wrap, and chill for at least 1 hour.
Preheat oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.
Dust rolling pin and cookie cutters with confectioners' sugar. Roll out dough to 1/2-inch thickness; cut cookies and place 2 inches apart onto the baking sheets.
Whisk egg yolk with food coloring and water in a small bowl. Decorate cookies with mixture using a child's paintbrush. Sprinkle sugar sprinkles on top.
Bake in the the preheated oven until edges are golden, 8 to 12 minutes. Cool on the baking sheets for 1 minute before removing to a wire rack to cool completely.
Nutritional Facts
Per 24 servings
Calories: 135
Carbohydrate: 21g
Fat: 6g
Fiber: 2g
Protein: 2g
Sugar: 10g
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