Preheat the oven to 350°F. Line a muffin pan with paper liners. In a large mixing bowl, combine the flour and baking powder. In another bowl, beat the butter and sugar until creamy, then add the eggs one at a time, mixing well. Stir in the vanilla and peppermint extracts.

Gradually add the flour mixture to the wet ingredients, alternating with milk, and mix until just combined. Avoid overmixing to keep the cupcakes light and fluffy.

Spoon the batter into the prepared liners, filling each about two-thirds full, and smooth the tops.

Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center comes out clean. Let them cool in the pan for a few minutes before transferring to a wire rack to cool completely.

Once the cupcakes are completely cool, prepare the frosting by beating the butter until smooth. Gradually add the powdered sugar, followed by the heavy cream and peppermint extract. Mix until the frosting is light and fluffy, then spread or pipe onto the cooled cupcakes. Finish with a sprinkle of crushed peppermint candies.

Store the frosted cupcakes in an airtight container at room temperature for up to three days, or refrigerate for up to a week. Allow them to come to room temperature before serving for the best flavor.