Preheat your oven to 350°F (175°C) and line a muffin tin with cupcake liners.

In a medium bowl, whisk together gluten-free all-purpose flour, baking powder, and salt.

Cream softened butter and sugar in a stand mixer on medium speed until light and fluffy, about 2-3 minutes.

Add eggs one at a time, mixing well after each addition. Pour in vanilla extract and blend until combined.

Gradually add the flour mixture to the wet ingredients, mixing on low speed until just combined.

Stir in milk and half & half until smooth. Fold in crushed candy canes.

Fill each cupcake liner about three-quarters full with batter. Bake for 25-30 minutes or until a toothpick comes out clean.

Let the cupcakes cool for about 5 minutes before transferring to a wire rack to cool completely.

In a mixing bowl, combine softened butter, vanilla extract, and half of the powdered sugar. Beat until creamy, then gradually add remaining sugar and half & half until smooth.

Frost each cooled cupcake with the peppermint frosting and top with reserved crushed candy canes.