Preheat oven to 350°F. Spray Bundt pan with vegetable oil spray, then lightly coat with flour. Set aside.
In the bowl of your mixer, combine cake mix, pudding mix, water, vegetable oil, sour cream, and eggs. Beat on low speed until just combined. Scrape the sides of the bowl with a rubber spatula, then beat for 3 minutes. Fold in chopped mints until combined.
Spoon batter into prepared Bundt pan. Spread evenly, then bake for about 50 minutes, until cake is set and a knife inserted in the center comes out clean.
Let cake cool in pan for about 15 minutes, then very carefully turn onto a wire rack to continue cooling.
In the bowl of your mixer, beat cream cheese, butter, and peppermint extract on medium speed until smooth.
Add powdered sugar and beat on medium low until combined.
Add milk and food coloring and increase mixer speed to high. Beat for one minute, until smooth.
Spoon frosting around the top of the Bundt cake, then spread with an offset spatula.
Place cake in the refrigerator to chill for at least 30 minutes.
In a large bowl, whisk together powdered sugar and cocoa powder until combined.
Add melted butter, vanilla, and water and whisk until smooth and thickened.
Drizzle over cooled frosted cake, then top with additional chopped mints, if desired.