In a mixing bowl, whisk together flour, baking powder, and salt. Set aside.
In the bowl of a standing mixer, beat the butter on medium-high until smooth.
Add sugar and beat on high until light and fluffy, ~2 minutes.
Add eggs one at a time, mixing between each addition. Add vanilla and mix for 1 minute more.
Add dry ingredients in three increments, mixing between each one.
Divide dough into three even portions.
Red. Put the first portion of dough in the mixer and add red food coloring / gel, while mixing, until the dough is a nice bright red. Set red dough aside and wipe out bowl.
Blue. Put the second portion of dough in the mixer and add blue food coloring / gel, while mixing, until the dough is a nice bright blue. Set red dough aside.
Working with one portion of dough at a time, roll each into a 11" x 11" square. (I use a permanent marker to draw a square on a piece of wax paper and use that as a guide. The squares don't have to be perfect, just generally around the same size.)
Refrigerate dough squares for 30 minutes until chilled (this will make them easier to layer without the colors bleeding together).
Remove dough from refrigerator and stack the three portions of dough (in any order). Gently press dough layers together.
Using the bottom sheet of wax paper to lift dough, roll it into a log. Press gently as you roll to avoid gaps. Wrap the dough tightly in wax paper.
Refrigerate for 2 hours or up to 5 days. (At this point the dough can be wrapped in foil and frozen for up to 3 months; defrost in the refrigerator for 2 to 3 hours before baking.)
Preheat oven to 375 degrees F.
If using sprinkles, remove the dough from the wax paper and roll in sprinkles to coat on all sides.
Using a sharp knife cut roll into 1/8" slices. Place slices on an ungreased baking sheet. The cookies will spread slightly as they bake, so leave ~2" between.
Bake until cookies appear just set in the middle, 8 to 10 minutes. (The texture will be tender and buttery. I've been known to bake these for as little as 6 minutes. Soft, gooey, delicious.)
Transfer to a cooling rack and allow to cool completely.
Store in an airtight container for up to 3 days.