In a large bowl, beat butter and sugar with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in extracts.
In a medium bowl, whisk together flour, baking powder, and salt. Gradually add flour mixture to butter mixture, beating just until combined. Divide dough in half; beat food coloring into one half. Wrap dough portions separately in plastic wrap, and refrigerate for 1 hour.
Roll each piece of dough between sheets of parchment paper to an 11x9-inch rectangle, about ¼ inch thick. Remove top pieces of parchment, and stack dough on top of each other. Roll layered dough to a 12x10-inch rectangle; trim edges with a pizza cutter or sharp knife. Starting at one long side, tightly roll dough into a log, using parchment to help roll. Refrigerate for 1 hour.
Roll dough log in nonpareils. Wrap in plastic wrap, and freeze for 30 minutes.
Preheat oven to 350°. Line baking sheets with parchment paper.
Unwrap dough, and trim ends. Using a serrated knife, cut log into ⅔-inch-thick slices; place 1 inch apart on prepared pans.
Bake until set, 12 to 15 minutes. Let cool completely on pans on wire racks. Store in an airtight container for up to 5 days.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/pinwheel-peppermint-sugar-cookies-recipe/