Preheat the oven to 350° Fahrenheit and grease a 9x13-inch cake pan with nonstick spray and set aside.
In a large bowl or stand mixer, whisk together the flour, sugar, cocoa, baking powder, baking soda, and salt in a large bowl.
Add eggs, milk, vegetable oil, and vanilla extract and beat on medium speed for 2 minutes.
Add in the hot espresso or coffee and mix until combined. The batter will be thin.
Pour the batter into the prepared 9x13-inch pan and bake for 35 to 40 minutes or until a toothpick comes clean when inserted into the center of the cake.
Remove the cake from the oven and poke holes all over it with a skewer.
Whisk together the sweetened condensed milk, evaporated milk, half & half, and hot chocolate mix in a medium bowl and then pour it over the top of the warm cake and allow it to sit for 1 hour at room temperature before frosting.
Prepare the frosting by adding the heavy cream, hot chocolate mix, sugar, vanilla, and peppermint to a large bowl or stand mixer and beating on medium-high speed thick and creamy. About 1 to 2 minutes.
Spread the frosting evenly over the cake and top with marshmallows, sprinkles, and Peppermint pieces.