Preheat your oven to 350°F (175°C) and prepare a cupcake tin with liners.
In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3-5 minutes.
Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla and peppermint extracts.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, alternating with the milk and mixing until just combined.
Gently fold in the white chocolate chips until evenly distributed.
Spoon the batter into the prepared cupcake liners, filling each about two-thirds full.
Bake in the preheated oven for 20-25 minutes or until a toothpick inserted into the center comes out clean.
Let the cupcakes cool in the tin for 10 minutes before transferring them to a wire rack to cool completely.
Prepare the frosting by beating the softened butter and powdered sugar together until creamy and fluffy, adding the heavy cream to adjust consistency as needed.
Frost the cooled cupcakes using a piping bag or a knife, creating generous, decorative swirls.
Finish by garnishing with crushed candy canes on top of the frosting.
