In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.

In a stand mixer fitted with the paddle attachment (or using a hand mixer), beat the butter on medium speed until smooth. Gradually add the sugar and continue mixing until light and fluffy, about 2 minutes.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract. With the mixer on low speed, add the dry ingredients in three additions, mixing just until combined.

Divide the dough evenly into three bowls. Leave one portion plain for the white layer. Tint one portion red and the other blue using gel food coloring, kneading gently until the color is evenly distributed.

Shape each portion into a flat rectangle. Wrap tightly in plastic wrap and refrigerate for at least 30 minutes, until firm but still pliable.

On a lightly floured surface, roll each dough portion into a rectangle of similar size. Stack the red layer on top of the white layer, then place the blue layer on top. Press gently so the layers adhere without blending the colors.

Starting from a short edge, roll the dough tightly into a log. Wrap and refrigerate for at least 2 hours or overnight to keep the pinwheels sharp.

Preheat the oven to 375°F (190°C). Line baking sheets with parchment paper.

Slice the chilled dough log into ¼-inch thick rounds. If desired, roll the edges in coarse sugar or sprinkles. Arrange cookies on the baking sheet with space between them.

Bake for 8–10 minutes, until the edges are just set and the centers remain soft.

Let cookies cool on the baking sheet for a few minutes, then transfer to a wire rack to cool completely. Store in an airtight container at room temperature for up to 4 days.