In a medium bowl, whisk together the flour, baking powder and salt.
In a large mixing bowl, cream butter and sugar together until mixture is light and fluffy, about 3 minutes.
Add the egg and beat it in. Then add the vanilla and beat again.
Add the flour and beat just until combined.
Remove the dough and separate it into three equal pieces.
Shape one piece of the dough into a 4x2 rectangle (approximate, just use eyes to guess close), wrap it securely in wax paper and place it in the fridge. (This will be the white portion of the cookies.)
Add other two portions of dough to two separate bowls. Color one dough portion red and mix until it's incorporated. Color the other dough portion blue, mixing again until it's incorporated. Add enough dye to get the colors that you want. Remember that dye will deepen slightly as it sits.
Form both red and blue dough into separate rectangles between wax paper as in step 6. Refrigerate all dough for 30 minutes.
Place the red dough in between two pieces of wax paper and roll it into a rectangle about 1/8-inch thick. Repeat separately for white and blue dough.
Peel the top layer of wax paper off of the red dough and then peel the wax paper off one side of the white dough and use the other side to transfer the white dough on top of the red dough. Peel off the wax paper from one side of the blue dough and use the other side to transfer it atop the white dough. Very lightly roll the three layers together using a rolling pin.
To get a perfect rectangle, take a sharp knife and cut off any edges that stick over a rectangle.
Starting at the shorter end of the rectangle, roll the dough as tightly as possible into a log. Wrap the log in wax paper. Stand the roll up in a glass in the fridge for 4 hours or freezer for 30 minutes. (I've included a picture of this. Standing them up prevents them from getting a flat side.)
When ready to bake, preheat the oven to 350ºF and line two baking sheets with parchment paper.
Remove the dough from the fridge and slice each log into 1/4-inch rounds. You'll get between 18-24 cookies. Place the rounds about 2 inches apart on the baking sheets, as the cookies will expand when baked. You may need to do more than 2 batches.
Bake the cookies for 9 to 11 minutes until pale golden. Try not to let them brown. Let sit on tray for 3-4 minutes before transferring to a cooling rack.
Store in an airtight container.
The calories shown are based on the recipe making 24 cookies, with 1 serving being 1 cookie. Since different brands of ingredients have different nutritional information, the calories shown are just an estimate. **We are not dietitians and recommend you seek a nutritionist for exact nutritional information.**