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In a medium bowl, whisk together flour, baking powder, and salt. In a large bowl using a hand mixer (or in the bowl of a stand mixer, fitted with a paddle attachment), beat butter and sugar together. Add egg and beat until incorporated, then add extract. Add dry ingredients and beat until just combined.
Divide dough in half, keeping one half in mixing bowl. Add red food coloring and mix until desired color is reached. Shape each dough into a square that is roughly ½” thick. Wrap in plastic wrap and refrigerate until firm, about 30 minutes.
Place red dough between two sheets of parchment paper and roll into a rectangle that’s about 1/4″ thick. Repeat with white dough. Take top sheet of parchment paper off of each dough. Place red dough on top of white dough, dough sides facing each other. Gently press on top of dough to help seal together.
Remove top parchment paper and trim sides to match up evenly. Starting on a long side, use the bottom parchment paper to help roll dough tightly in to a log. Roll log on the counter a few times to help seal the edge. Wrap in plastic wrap and refrigerate until firm, at least 1 hour and up to overnight.
Preheat oven to 350°. Line 2 large baking sheets with parchment paper. Place sprinkles on a medium plate. Using a sharp knife, slice cookies 1/2” thick and roll edges in sprinkles. Place on baking sheets 2” apart.
Bake until edges are set and just starting to turn golden, 10 minutes.