In the bowl of a stand mixer, beat together the sugar and butter until fluffy. Mix in the egg, salt, vanilla and baking powder. Sift in the flour and beat until a soft dough forms.
Divide the dough into three equal portions. When not working with the dough, keep it wrapped in plastic and chill in the fridge. Take a single portion and mix in the red food coloring until the dough is a sufficient red color. Repeat with the green food gel and another portion of dough. Leave the final portion plain. Wrap all three, separately, in plastic wrap and chill for at least and hour.
Lightly flour a smooth surface. Working on one color at a time, roll the dough thin. Once it's about half a centimeter in thickness, transfer the sheet of dough onto plastic wrap and press a second piece of plastic wrap on top. I placed each of these flattened layers on a cookie sheet and chilled for another hour.
Take all three sheets of dough out of the fridge. Remove the plastic wrap and sandwich the plain/white layer between the red and green layers. Gently press the layers together. Trim the edges so that they are all straight. Roll the layers of dough into a log shape. Wrap plastic tightly around the dough and chill again for at least an hour.
Preheat the oven to 350 F. Remove the dough from the plastic wrap and cut into pieces an even 1/2 inch thickness. Arrange the cookies on a baking sheet lined with parchment or silicone mats. Bake for 8-10 minutes, until the cookies are puffed up and cooked through.
Let the cookies rest on the baking sheet for a few minutes after removing them from the oven. They will finish baking on the hot tray. After about ten minutes, transfer the cookies to a wire rack to cool completely. Enjoy!