Beat butter and sugar until fluffy, add peppermint extract.
In another bowl, stir together the all purpose flour with the rice flour.and add butter mixtue in three additions stirring well to combine.Stir in candy canes
Gather dough together and divide into 4 discs. Roll each disc between two pieces of parchment paper to a 1/4 inch thickness.Cut out cookies using a 3 inch round cookie cutter and place on a parchment paper lined baking sheet. Freeze for 15 minutes or until firm.
Preheat oven to 275
Bake 1 tray at a time on the centre rack of the oven for appx 30 minutes and let cool on rack for 5 minutes.
Remove cookies to cooling rack to let cool completely.