Preheat oven to 350°F. Line a 9x13-inch baking dish with a parchment paper sling or spray with baking spray.
In a large mixing bowl, beat the butter and sugar until creamy and light. Add the eggs and vanilla extract, beating again and stopping to scrape the bottom and sides of the bowl until everything is well mixed.
1 cup (227g) salted butter, 2 cups (400g) granulated sugar, 4 large eggs, 2 teaspoons vanilla extract
Add flour, cocoa powder, baking powder, and salt. Stir just until combined, then spread into the prepared pan.
1 cup (141g) all-purpose flour, ⅔ cup (58g) natural unsweetened cocoa powder, ½ teaspoon baking powder, ½ teaspoon salt
Bake 25 to 30 minutes until a toothpick inserted into the center of the brownies comes out almost clean with just a little batter or a few crumbs on it. Remove the brownies from the oven and sprinkle with marshmallows. Return the brownies to the oven and bake for 3 to 5 minutes until marshmallows are puffy and the brownies are just done. Cool before frosting.
1 (10-ounce) bag miniature marshmallows
When the brownies have cooled, combine the butter, cocoa powder, powdered sugar, and evaporated milk in a medium mixing bowl Beat the frosting ingredients with a hand mixer until creamy and light, then spread over the cooled brownies. Cut into squares.
½ cup (113g) salted butter, ¼ cup natural unsweetened cocoa powder, 3 cups (360g) powdered sugar, ⅓ cup evaporated milk, 1 teaspoon vanilla extract