Preheat oven to 350°. Microwave chocolate in a microwave-safe bowl at MEDIUM (50% power) 1 1/2 minutes or until melted and smooth, stirring at 30-second intervals.
Beat 1 cup butter and 2 cups granulated sugar at medium speed with an electric mixer until light and fluffy. Add 4 eggs, 1 at a time, beating just until blended after each addition. Add melted chocolate, beating just until blended. Add 1 cup flour, beating at low speed just until blended. Stir in vanilla. Spread half of batter in a greased and floured 13- x 9-inch pan.
Beat peanut butter, brown sugar, and remaining 1/3 cup butter and 1/2 cup granulated sugar at medium speed with an electric mixer until light and fluffy. Add 2 eggs, 1 at a time, beating just until blended after each addition. Stir together baking powder and remaining 1 cup flour, and add to peanut butter mixture, beating at low speed just until blended.
Spoon peanut butter mixture over brownie batter; top with remaining brownie batter, and swirl together.
Bake at 350° for 45 to 55 minutes or until a wooden pick inserted in center comes out with a few moist crumbs. Remove from oven to a wire rack; sprinkle with marshmallows and peanuts.
Cook butter, cocoa, and milk in a saucepan over medium heat, whisking constantly, 4 minutes or until slightly thickened; remove from heat. Whisk in powdered sugar and vanilla until smooth.