IGNORE the directions on the brown mix box!
Preheat the oven to 350F degrees.
Line a nonstick 13x9 baking pan or baking dish with parchment paper or aluminum foil. If using aluminum foil or a pan that is not nonstick, spray with vegetable cooking spray. You can also grease the pan and foil. No need to grease parchment paper. Lightly beat the eggs together with a sturdy spoon in a large bowl. No need for a hand mixer. Add oil and water stirring well to combine. Then, stir in the brownie mix until combined. Stir vigorously about 40 times.
Pour the brownie batter evenly into the parchment paper or foil lined pan, spread to the edges.
Bake, uncovered, for 18 minutes. (SEE NOTES for baking time for 9x9 pan.) A toothpick inserted in center will not come out clean but should not be completely wet either. Brownies will firm up as they cool.
Remove the pan of brownies from the oven and place on a wire rack or on your stovetop. Immediately sprinkle the mini marshmallows evenly over the hot brownies. Immediately cover with aluminum foil or the pan's lid if it has one.Remove the foil after 8 minutes.This step is important to melt the marshmallows just enough! Spoon the frosting into a microwave-safe bowl. I like to use a glass measuring cup because it has a pouring spout on it. Microwave on HIGH for 25 seconds, then stir well. It should be a good pouring consistency. If it is a bit too thick, try 4 more seconds. (SEE NOTES to melt frosting on the stovetop.)
Drizzle the frosting over the partially melted marshmallows. I start in one corner and drizzle half the frosting across the pan, then start in the opposite corner and drizzle across the other side. This allows some of the marshmallows to show through on the top.
Allow the brownies to cool to room temperature. They are ready to eat, now, but they cut MUCH easier if refrigerated at least 1 hour first. I like to chill them for 2 hours.
Carefully lift the brownies out of the pan with the parchment paper or foil. Place on a cutting board and cut into desired number of pieces. Calories are calculated below for 15 pieces.
Store the brownies, covered, in the refrigerator so they will stay fresh longer and cut more easily. They can also be stored at room temperature. Enjoy!