Preheat oven to 350°F. Spray a 15‑in. x 10‑in. x 1‑in. baking pan with nonstick spray.
In a large mixing bowl, use an electric mixer to beat 1½ cups granulated white sugar and 3/4 cup (1½ sticks) butter (at room temperature) until light and fluffy, about 2–3 minutes. Add the 3 large eggs and 1 teaspoon vanilla extract, mixing until well combined and the mixture is again light.
In a medium bowl, whisk together 1 1/3 cups all‑purpose flour, 3 tablespoons unsweetened cocoa powder, 1/2 teaspoon baking powder, and 1/2 teaspoon salt.
Add the dry ingredients to the butter mixture and mix on low speed just until combined; do not overmix.
Spread the batter evenly into the prepared pan. Bake 15–18 minutes, or until the top is set and a toothpick inserted in the center comes out with moist crumbs (not wet batter).
Remove the pan from the oven. Evenly sprinkle 4 cups mini marshmallows over the baked layer. Return the pan to the oven for 2–3 minutes, watching closely, until the marshmallows have softened and begun to melt.
Remove the pan again. Dip a knife in warm water and wipe it dry, then use the knife to gently spread the melted marshmallows into an even layer over the first layer. Let the pan cool until the marshmallow layer is set to the touch.
For the topping, place 8 ounces milk chocolate chips, 3 tablespoons butter, and 1 cup peanut butter in a medium saucepan over low heat. Cook, stirring frequently, until the mixture is completely melted and smooth. Remove from heat.
Stir 2 cups Rice Krispies into the melted chocolate–peanut butter mixture until evenly coated. Immediately spread this mixture evenly over the marshmallow layer and smooth to level.
Chill the assembled bars until the topping is firm. Cut into bars and serve.