To make the cookies:
In a bowl whisk together the flour, baking powder and salt, set aside.
In a stand mixer, fitted with the paddle attachment, cream the butter and sugar together until light and fluffy, about 2 minutes. Add the eggs, one at a time, mixing on medium speed until well incorporated. Mix in the extracts and zest.
Add the dry ingredients and mix just until it comes together and no flour is visible. Divide the dough into two or three packets and refrigerate the dough until set, about an hour. Can be frozen for up to a month.
To bake the cookies:
Preheat the oven to 350 degrees F. Line baking sheets with parchment paper.
Using enough flour to prevent the dough from sticking, but not too much or the cookies will be tough. Roll it out to about 1/8-inch thick circle. Use a star shaped cookie cutter to cut out the cookies.
Set them on the prepared baking sheets, leaving some space between them. Bake for about 8 minutes, or until just golden on the bottoms.
To make the royal icing:
Combine all the ingredients for the icing in the bowl of a stand mixer, fitted with the whip attachment. Blend together on low speed until all the sugar is blended with the lemon juice, then turn it up to medium-high and whip to stiff peaks.
Divide the icing into separate bowls, how many will be determined by the colors you are making. Add the food coloring to create the color you desire. Make sure to cover the bowls with plastic wrap so the icing will not harden.
For simple decorations:
Spread a thin layer of the icing over the cookie. While the icing is still soft, sprinkle the cookie with the icing sugar. Do this over a paper plate so you don't make a mess and waste the sugar.
To make a more sophisticated design:
Fill a paper pastry bag with some of the icing and cut a small hole at the tip. Trace the outline of the cookie with the icing.
In a small bowl combine the icing you want to use as the filler with a bit of water, to create an icing that will flow. Start with just a few drops and add more as needed. It should be the consistency of slightly thin honey.
Fill another pastry bag with the thin icing and carefully fill in the center of the cookie, being careful not to put so much that it goes over the outline.
While the filling is still wet, sprinkle it with the icing sugar. Be sure to leave the cookie flat until it sets hard. Once the icing is set, which can take an hour or more, they are safe to stack.