Preheat your oven to 350°F (175°C). Grease your 9x13 inch baking pan or line it with parchment paper for easy removal.
In a large mixing bowl, combine the boxed brownie mix, 1/4 cup of water, 2/3 cup of oil, and 2 large eggs. Mix until well combined and smooth.
In another bowl, beat together the softened cream cheese, 1 egg, granulated sugar, softened butter, all-purpose flour, and 1 teaspoon of vanilla extract. Mix until the mixture is creamy and smooth.
Pour half of the brownie batter into the prepared baking pan, spreading it evenly. Then, dollop the cream cheese mixture on top and gently spread it out.
Pour the remaining brownie batter over the cream cheese layer and gently spread it out.
Sprinkle the milk chocolate chips, chopped nuts, and mini marshmallows evenly over the top. Press them down gently.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
While the brownies are baking, prepare the frosting by melting the butter, milk, and unsweetened chocolate in a saucepan. Let it cool slightly.
In a mixing bowl, beat together the cream cheese, powdered sugar, and vanilla extract. Gradually add the melted chocolate mixture until smooth.
Once the brownies are out of the oven, pour the frosting over the top and spread it evenly. Let the brownies cool completely before cutting them into squares.