To Make the Cookie Dough:

1. In a medium bowl, whisk together the gluten-free flour, baking powder and salt.  Set aside.
2. In a mixer bowl, cream the butter and sugars together until light and fluffy, about 1 to 2 minutes.
3. Add in the egg, vanilla, and milk. Mix until well combined.
4. Slowly add in the dry ingredients. Mix until well combined.
5. Gather the dough into a ball and wrap in plastic wrap or a plastic bag. Chill the dough in the refrigerator 2 hours or overnight.

Make the Cookies:

1. Preheat oven to 350°F. Line two baking sheets with parchment paper. Remove the dough from the refrigerator and allow to set at room temperature 10 to 15 minutes.
2. Sprinkle flour onto your rolling surface and the rolling pin. Lay the dough out and sprinkle a little flour on top.
3. Roll the dough out to about 1/4-inch thickness, adding more flour as needed to prevent sticking.
4. Use Christmas and Hanukkah cookie cutters to cut out shapes and place them on the baking sheets, leaving a two-inch space between cookies.
5. Gather remaining dough scraps and re-roll. Continue to re-roll and cut out shapes until all the dough has been used. Bake in batches as cookie sheets fill up.
6. Bake the cookies at 350°F 12-14 minutes. For crisper cookies, allow the cookies to get lightly browned. For not so crisp cookies, pull them from the oven before they brown.
7. Cool completely before frosting.

Make the Cookie Glaze:

1. Sift powdered sugar into a medium bowl. Add 6 teaspoons milk, corn syrup, and extract. Stir vigorously until glaze is smooth.
2. If needed, add additional milk to thin the glaze more. You've reached the correct consistency for the glaze if a scoop of icing slowly falls off the spoon.
3. Divide the glaze into two bowls and add green food coloring into one bowl, and blue food coloring into the other. Stir well until no white glaze appears in the mixture.

Glaze and Decorate the Cookies:

1. Add the glaze into two different piping bags with a small tip. Pipe an outline of each cookie and fill it in for pristine edges. Alternatively, it can also be spread with a small knife.
2. Decorate the cookies with your favorite sprinkles. This frosting hardens quickly so have sprinkles ready to put on immediately.
3. Before stacking or wrapping cookies, make sure the glaze is completely hard. Set cookies on a baking sheet for several hours and serve immediately or freeze in baggies for up to two months.