Preheat oven to 350F (176C). Spray a 9x13-inch (23x33cm) baking pan with cooking spray.
Melt butter in a small saucepan over medium heat, swirling pan occasionally. Once the butter foams, stir occasionally. Continue to cook until bubbles appear on the surface and the butter appears golden brown when stirred.
Immediately transfer to a large, heat-proof bowl and set aside to cool for 10 minutes.
Whisk together flour, baking powder and salt in a medium bowl. Stir in chocolate, walnuts and marshmallows.
Beat sugars into the cooled butter with a hand mixer until well combined in a large bowl.
Add eggs, one at a time along with vanilla into sugar mixture. Stir in the flour mixture until combined. Spoon the batter into the prepared baking pan and spread evenly into pan.
Bake until the edges are golden and the middle is set, about 30 to 35 minutes. Cool and cut to serve.