Preheat your oven to 325 degrees F. Spray a 10-cup bundt pan with Pam’s Baking Spray and set it aside.
In a stand sized mixer fitted with the paddle attachment, combine the flour, sugar, cocoa powder, baking soda, baking powder, and salt. Mix on low until evenly combined.
In a small bowl, whisk the eggs, buttermilk, hot water, peppermint extract, and vegetable oil until evenly combined.
With the mixer on the lowest speed, pour the liquid ingredients into the dry ingredients and mix just until combined. There should be no flour streaks. With a rubber spatula, scrape the bottom of the bowl to make sure the batter is evenly combined.
Pour the batter into the prepared bundt pan. Bake for 50-55 minutes (or until a toothpick inserted in the center comes out with only a few moist crumbs). Mine took 45 minutes but my oven runs warmer.
Allow the bundt cake to cool for 20 minutes before transferring it out of the bundt pan and to a cake plate or board. Let the cake cool for 30 minutes.
When the cake is ready, make the frosting.
For the frosting
In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese on medium speed until smooth, scrape the bottom and sides and continue to beat for 30 seconds. Add the rest of the ingredients, and mix on low speed until the powdered sugar is mixed in. Turn the mixer to medium-high speed and mix for a 1-2 minutes.
I used a piping bag to pour over the bundt cake, but you can use whatever a spoon or a bowl with a spout.
If you want a thick buttercream, instead of a thin icing, you can use the same recipe but simply use room temperature butter instead of melted butter.