In bowl of stand mixer or with electric beaters, beat butter, ½ cup (125 mL) of the icing sugar and the peppermint extract until creamy. In a separate bowl, whisk flour, cornstarch and salt; stir half into butter mixture. Stir in remaining flour mixture just until combined.
Lightly roll into 2 tsp (10 mL) balls; place 2 inches (5 cm) apart on a parchment-paper-lined baking sheet.
Bake in a preheated 300°F (150°C) oven until firm, 14 to 16 minutes.
Meanwhile, in a food processor, pulse remaining ½ cup (125 mL) icing sugar with candy canes until finely ground and powdery; pour into a small bowl.
Let cookies cool on pan on rack for no more than 5 minutes. Roll cookies in candy cane-icing sugar mixture while still warm. Let cool completely on pan.
Per cookie: 94 calories, 1 g protein, 6 g fat (4 g saturated fat), 10 g carbohydrates, 0 g fibre, 15 mg cholesterol, 20 mg sodium