Preheat the oven to 350°F (175°C).
Line a muffin pan with cupcake liners.
In a large mixing bowl, cream the softened butter and granulated sugar together until light and fluffy.
Add the eggs one at a time, beating well after each addition, then mix in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry mixture to the creamed mixture, alternating with the whole milk. Begin and end with the flour mixture.
Fold in the white chocolate chips gently until just combined.
Spoon the batter into the prepared cupcake liners, filling them about two-thirds full.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and allow the cupcakes to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
While the cupcakes are cooling, prepare the frosting by creaming softened butter until fluffy.
Gradually add the powdered sugar, mixing until combined, then mix in the peppermint extract.
Add the crushed peppermint candies and mix until evenly distributed.
Frost the cooled cupcakes generously and top with additional crushed peppermint candies if desired.