Preheat oven to 350°. Line a 13x9-inch baking pan with foil, letting excess extend over sides of pan; spray foil with cooking spray.
In a large microwave-safe bowl, melt butter on high in 30-second intervals, stirring between each, until smooth (about 2 minutes total). Let cool for 5 minutes. Add sugar, eggs, and vanilla, whisking until smooth.
In a medium bowl, whisk together flour, cocoa, baking powder, and salt. Gradually add flour mixture to butter mixture, whisking until smooth. Spread batter into prepared pan.
Bake until a wooden pick inserted in center comes out clean, 20 to 25 minutes. Let cool for 10 minutes. Spread peanut butter on top, and sprinkle with marshmallows and pecans. Bake until marshmallows are just soft, about 2 minutes more. Let cool completely in pan on a wire rack.
Spread Chocolate Frosting onto marshmallow layer. Cover and refrigerate until frosting is set, about 30 minutes. Using excess foil as handles, remove from pan, and cut into squares.
Notes
Baking Tip: Brownies can be prepared through step 4 and frozen for up to 1 month. Let them thaw completely at room temperature before frosting as directed.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/mississippi-mud-brownies-recipe/