Preheat your oven to 350°F (175°C) to ensure even baking.
Grease a 9x13 inch baking pan with butter or line it with parchment paper for easy removal.
In a large mixing bowl, cream together granulated white sugar and softened butter using a whisk until light and fluffy, about 2-3 minutes.
Add the eggs one at a time, mixing well after each addition, then stir in vanilla extract until combined.
In another bowl, whisk together all-purpose flour, unsweetened cocoa powder, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, stirring gently until just combined. Avoid overmixing.
Gently fold in the mini marshmallows, ensuring even distribution throughout the batter.
Pour the batter into the prepared baking pan and spread evenly with a spatula.
Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
While baking, melt milk chocolate chips and 3 tablespoons of butter together in a small saucepan over low heat. Stir until smooth and creamy. Remove from heat and stir in peanut butter until well combined.
Add Rice Krispies to the chocolate-peanut butter mixture, folding gently to coat evenly.
After bars have cooled for about 10 minutes, pour the chocolate mixture over the top and spread evenly with a spatula.
Let the bars cool to room temperature, then refrigerate for at least one hour to set the chocolate. Once set, cut into squares and serve.