Whisk together the flour, baking powder, and salt.

In a separate bowl, beat the butter and sugar for 2–3 minutes until smooth and creamy without excessively whipping the mixture. Mix in the egg and vanilla.

Gradually add the dry ingredients, mixing just until the dough comes together.

Divide the dough into three equal portions. Leave one plain, tint one red, and tint one green, gently kneading until evenly colored.

Roll each portion between parchment sheets into an approximately 9 × 12-inch rectangle, about ⅛ inch thick. Refrigerate for 10–15 minutes if too soft to handle.

Stack the dough with plain on the bottom, red in the middle, and green on top, removing parchment between layers. Gently roll over the stack to adhere the layers and trim ragged edges.

Starting at a long edge, roll into a snug log, using the parchment to guide the dough and peeling it away as you roll. Avoid trapping air between layers.

Wrap tightly, gently round the log, and refrigerate for about 2 hours, until very firm.

Unwrap and roll the log in sprinkles, pressing gently to attach them. Refrigerate for another 20–30 minutes.

Preheat the oven to 350°F. Line baking sheets with parchment.

Slice the log into ¼-inch rounds with a sharp knife, rotating it occasionally to maintain its shape. Arrange about 1 inch apart. If softened, refrigerate the slices for about 10 minutes, or until firm, before baking.

Bake for 10–12 minutes per batch, until the edges are barely beginning to turn golden. Keep unbaked dough chilled between batches.

Cool on the baking sheet for 5 minutes, then transfer carefully to a wire rack to cool completely.

Notes