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Preheat oven to 350 F.
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Line a nonstick 9x13 baking dish with parchment paper or aluminum foil. If using foil spray with non-stick cooking spray.
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Lightly beat the eggs together with a spoon in a large bowl. Add the oil and water stirring well to combine. Then stir in the brownie mix until combined. Stir vigorously about 40 times.
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Pour the brownie batter evenly into the lined baking dish, spread to the edges.
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Bake, uncovered, for 18 minutes. A toothpick inserted in the center comes out almost clean. Brownies will firm up as they cool.
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Remove the pan of brownies from the oven and place on a wire rack. Immediately sprinkle with mini marshmallows evenly over the hot brownies. Immediately cover with aluminum foil.
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Remove the foil after 8 minutes.
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Spoon the frosting into a microwave safe bowl or a glass measuring cup. Microwave on HIGH for 25 seconds, then stir well. It should be a good pouring consistency. If too thick, microwave 4 seconds more.
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Drizzle the frosting over the partially melted marshmallows. Start in one corner and drizzle half of 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 the top.
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Allow the brownies to cool to room temperature. Then refrigerate at least 1 hour.
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Carefully remove the brownies out of the pan with the parchment paper or foil. Place on a cutting board and cut into desired number of pieces.
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Store the brownies, covered, in the refrigerator.