Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Sift flour, cocoa powder, baking powder, and salt together in a large bowl. Beat sugar, butter, and vanilla extract together in a separate bowl; beat in eggs, one at a time, until sugar mixture is smooth. Stir flour mixture into sugar mixture until incorporated. Spread batter into the prepared baking pan.
Bake in the preheated oven until a toothpick inserted in the center of the brownies comes out clean, about 20 minutes.
Mix peanut butter and chocolate chips together in a microwave-safe bowl; heat in microwave until chocolate chips are melted, stirring every 30 seconds, 1 to 2 minutes. Fold crispy rice cereal into peanut butter mixture; heat in microwave until mixture smooth and spreadable, about 30 seconds.
Sprinkle brownies with marshmallows and bake until marshmallows are slightly cooked, 2 minutes. Pour chocolate mixture evenly over marshmallows. Allow to cool completely before cutting into squares.