Whisk flour, baking powder, and salt. Beat butter and sugar until fluffy, about 2 minutes, then beat in egg and vanilla. Mix in dry ingredients just until combined.

Divide dough in half. Tint one half red with gel coloring, adding almond extract if using. Tint the other green, adding peppermint extract if using. Shape each into a disc, wrap, and refrigerate at least 2 hours.

Roll red disc between parchment to a 10x12-inch rectangle, 1/8 inch thick. Chill while rolling green dough to the same size. Layer green on top of red, peel off parchment, and chill if soft.

Starting from a long edge, use the parchment to roll the layers tightly into a log. Wrap and chill at least 1 hour until very firm.

Preheat oven to 350°F (175°C). Slice log into 1/4-inch rounds, place on parchment-lined sheets, and bake 10 to 12 minutes until edges are barely golden. Cool on sheet 5 minutes, then transfer to a rack.

Cool cookies completely on a wire rack before serving or storing.