In a large mixing bowl, combine the boxed cake mix, instant pudding mix, eggs, vegetable oil, and hot water. Mix on medium speed until well blended.
Preheat oven to 350°F (175°C). Grease bundt pan and pour batter in. Bake for 40-45 minutes or until a toothpick comes out clean.
Remove from oven, cool for 10-15 minutes in the pan, then invert onto a wire rack to cool completely.
In a mixing bowl, combine sifted powdered sugar, softened butter, peppermint extract, and milk. Beat until smooth and spread over the cooled cake.