Cream butter; gradually add sugar, beating until light and fluffy.
Add egg and peppermint extract, beat well.
Combine next 3 ingredients, add to mixture, beating just until blended.
Divide dough in half; add a few drops red food coloring to one half, and knead until color is distributed.
Cover and refrigerate both halves until firm.
Divide each portion of dough into 2 equal portions.
On floured waxed paper, roll one white portion and one red portion into an 8-inch square.
Invert white dough onto red dough, peel waxed paper from white dough.
Tightly roll dough jellyroll fashion, peeling waxed paper from red dough as you roll.
Repeat with remaining dough.
Cover with waxed paper, and chill.
Cut dough into 1/4-inch slices, place on ungreased baking sheets.
Bake at 350Â° for 10 minutes.
Remove to wire racks to cool.