In a medium bowl, sift together the flour, baking powder and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter until smooth, about 2 minutes. Add the sugar and continue beating until light and fluffy. Add the eggs one at a time, beating between each addition and stopping the stand mixer to scrape down the sides as needed. Beat in the vanilla extract.
Turn the mixer off then add the flour mixture and beat just until combined. Remove the dough and divide it in half.
Return half of the dough to the stand mixer along with your desired amount of red food coloring. Mix until the dough is a cohesive red color. Transfer the dough to plastic wrap, shaping it into an 8-inch square. Wrap it securely and place it in the fridge. Repeat the coloring process with the other half of dough, mixing it with your desired amount of green food coloring. Wrap the green dough in plastic wrap and refrigerate both doughs for 30 minutes.
Remove the doughs from the fridge and cut each in half to form two rectangles of red dough and two rectangles of green dough. Refrigerate one red and one green piece of dough while you roll out the others.
Roll each piece of dough between two pieces of wax paper until it is a rectangle about 1/8-inch thick. Peel off the top layer of wax paper from the green dough then invert it atop the red, peeling off the wax paper so that you have red and green dough stacked atop one another. Lightly roll the two layers together then trim the shorter end of the rectangle so that you have a straight line. Starting on the shorter (trimmed end), roll the dough up, peeling off the wax paper as you tightly roll. Wrap the dough log securely in plastic wrap and refrigerate it for 1 hour. (To avoid a flat edge, roll the dough log every 20 minutes.) Repeat the rolling, stacking and refrigerating process with the remaining two pieces of dough.
Place the sprinkles in a large shallow pan. Remove the plastic wrap from the dough logs then roll them in the sprinkles.. Re-wrap the dough logs in plastic wrap and refrigerate them an additional 2 hours until firm. (At this point, the dough logs can be stored in the fridge for up to 1 week if wrapped securely in plastic wrap.)
When ready to bake, preheat the oven to 350°F and line two baking sheets with parchment paper.
Remove the dough from the fridge and slice each log into 1/4-inch rounds. Arrange the cookies on the baking sheet, spacing them about 2 inches apart.
Bake the cookies just until set, 9 to 11 minutes. Remove them from the oven then let them cool on the baking sheets for 5 minutes before transferring them to a rack to cool completely.