Whisk the flour, baking powder and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Beat in the egg and vanilla until incorporated. Reduce the mixer speed to low; add the flour mixture and beat until just combined. Remove half of the dough and wrap in plastic wrap. Add the cinnamon extract, cocoa powder and food coloring to the remaining dough and beat until incorporated; wrap in plastic wrap. Refrigerate both pieces of dough until firm, about 1 hour.
Dust the dough with flour and roll out each piece on parchment paper into a 10-by-11-inch rectangle. Flip the red dough on top of the plain dough; remove the top piece of parchment and trim the edges. Sprinkle the ground cinnamon and sanding sugar on top. Starting from a short end, tightly roll up the dough, using the parchment to help; roll the log in sanding sugar. Wrap in plastic wrap and refrigerate until firm, at least 3 hours or overnight.
Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment. Slice the log crosswise 1/4 inch thick; arrange the slices about 1 1/2 inches apart on the baking sheets. Bake, switching the position of the pans halfway through, until slightly puffed and lightly golden on the bottom, 12 to 15 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool.