Preheat the oven to 350F.
Mix together all of the dry ingredients (all-purpose flour, sugar, brown sugar, unsweetened cocoa powder, baking powder, baking soda, and salt) in a large mixing bowl using a whisk.
Add vegetable oil, eggs, whole milk, sour cream, and vanilla extract to the dry ingredients. Mix together using an electric mixer at low speed. Then, slowly add boiling water while beating.
Grease a 9x13-inch baking dish with nonstick cooking spray. Then, transfer the chocolate batter to the greased baking dish. Bake in the preheated oven for 25-30 minutes or until ready. Check the readiness of the chocolate mud cake using a toothpick inserted in the center, if it comes out clean - the cake is ready.
Remove your easy Mississippi mud cake from the oven and top with mini marshmallows. Then, return the chocolate mud cake to the hot oven. Bake for additional 2-4 minutes or until mini marshmallows is puffed and lightly browned. Remove the baking dish from the oven and let it cool to room temperature.
While the chocolate mud cake is cooling, prepare the chocolate topping. In a saucepan, melt unsalted butter. Then, stir in the whole milk and unsweetened cocoa powder. Cook, stirring constantly until the mixture is completely heated and combined (usually it takes about 2-3 minutes). Then, remove the saucepan from the heat, add vanilla extract and slowly add powdered sugar, beating after each addition using an electric mixer. Pour over the cooled chocolate mud cake. Place the cake in the refrigerator to set the topping. Then, slice and enjoy!