Preheat the oven to 350 degrees.
Prepare a 9x13 pan by spraying it with cooking spray, and lining it with parchment paper.
Melt the butter (1 cup), and let cool. To a mixing bowl, add the butter, vegetable oil (2 T.), granulated sugar (1 1/4 cups) and brown sugar (1 cup), and mix well.
Whisk in the eggs and vanilla, beating the batter until it's lighter in color, which takes about a minute.
Add the flour (1 cup), cocoa powder (1 cup), and salt, then mix only until combined. Pour in the chocolate chips (8 oz.) and fold in gently.
Pour the batter in to the prepared pan, and bake for 30-35 minutes, or until brownies are set and a toothpick comes out clean (and not jiggly in the middle). As soon as the brownies come out of the oven, sprinkle the marshmallows (3 cups) evenly over the top. Place back in the oven for about 2-3 minutes just until the marshmallows look puffy. Remove from the oven and let cool completely.
While the brownies are cooling, start your frosting. Measure the powdered sugar (3 cups) into a large mixing bowl.
In a large glass measuring cup, or glass bowl (microwave safe), melt the butter (1/2 cup), cocoa (4 T.), and 2 tablespoons of the milk until it comes to a boil. Stir in the vanilla, then add the chocolate mixture to the powdered sugar.
Add the rest of the milk, beating with a wooden spoon until the consistency is smooth.
Add a little more milk if necessary, or until you have the frosting consistency you'd like.
Pour the frosting over the marshmallows, and spread evenly across the top.