Preheat the oven to 300 degrees F. Insert liners into a medium cupcake pan.
In a large bowl cream together the butter and sugar with an electric mixer on medium speed until fluffy, 3-5 minutes.
In a separate bowl, with clean beaters on medium speed beat the eggs and peppermint extract together.
Add the egg mixture to the creamed mixture.
In a separate bowl combine the flour, baking soda, and salt.
Gradually add the dry ingredients to the creamed mixture, alternating with the milk. Do not overmix. Sprinkle the ground peppermint candies into the batter. Add the boiling water and partially melt the candies. Mix slightly.
Fill the cupcake liners ¾ full. Bake for about 20 minutes or until a toothpick inserted in the center of cupcakes come out clean. Cool cupcakes in the pan.
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