In a large mixing bowl, cream together the butter and the powdered sugar until fluffy.
Add the egg, vanilla extract, peppermint extract, and salt. Mix until well combined.
Add the flour and mix until well combined.
Divide the dough in half and stir the red food coloring into 1/2 of the dough portion. Wrap and chill up to 30 minutes.
Remove the dough from the refridgerator and preheat the oven to 375 degrees.
Divide the red and the white dough into 1 teaspoon portioned sizes. Roll each portioned dough into a 4" rope.
Place 1 white and 1 red rope side by side and stiwt them together, pinching the ends to seal. Form the twisted rope into a candy cane. Place the cookies 2" apart on a cookie sheet that has been lined with parchment paper.
Bake for 8 minutes or until cookies are firm to the touch. Remove and cool.