Position racks in the upper and lower thirds of the oven; preheat to 300 degrees F.
Whisk the flour, baking powder, cayenne and salt in a medium bowl.
Beat the butter and sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Beat in the egg, cinnamon extract and food coloring until smooth. Reduce the mixer speed to low; beat in the flour mixture until combined.
Fill a cookie press with the dough according to the manufacturers' instructions. Press cookies 1 inch apart onto 2 unlined baking sheets. Lightly press silver dragées into each.
Bake, switching the pans halfway through, until the cookies are firm to the touch, 25 to 30 minutes. Loosen the cookies immediately with a thin spatula and transfer to a rack to cool completely. Repeat with the remaining dough.