Combine flour, salt & baking powder in a bowl, mix and set aside.
In another large mixer bowl, cream together the softened butter & sugar.
Once smooth, add the eggs & vanilla and beat well.
Add the flour mixture to the butter mixture a little at a time. Mix until the dough is smooth and flour is fully incorporated.
Separate your dough into three equal parts.
Flatten one ball of dough into a disk or rectangle, wrap it in plastic wrap, and set it in the fridge.
This will be your plain, white dough.
Color one of the remaining portions of dough red, and one blue. Use the mixer to beat the color into the dough until you have reached the desired shade of each color. Be sure to rinse out the bowl and the beater inbetween the colors so that you don't cross the colors and end up with purple.
Flatten both of those into rectangles or disks, wrap in plastic, and allow all three portions of dough to firm up in the refrigerator for about an hour or two.
Roll out each ball of dough to about ⅛ - ¼" thick, and stack them one on top of the other (I did red on the bottom, followed by white, and then blue).
Trim the edges with a pizza cutter so you have nice, straight edges.
If desired - Pour some sprinkles into your hand & brush the outside of the dough with a bit more water and then press the sprinkles into the outside of the dough log.
Roll the dough into a log, wrap in plastic wrap and chill in the refrigerator for at least 1 hour.
Preheat the oven to 350 degrees.
Cut the log of dough into ¼ - ½" thick cookies and place on a parchment lined baking sheet - approx 2 inches apart. The thinner the blade used to slice them, the better. A thick blade will tend to squish the dough.
Bake at 350 for 10-12 minutes, or until no longer shiny on top.