Preheat the oven to 350 degrees. Line a 9X13-inch baking pan with aluminum foil or parchment paper and lightly spray with cooking spray (helps with cleanup and lifting out the bars).
For the brownies, in a medium saucepan over low heat or in a microwave-safe bowl in the microwave, melt the butter and chocolate chips. Stir constantly and remove from the heat when the chips are fully melted.
Whisk in the sugar and vanilla. Add the eggs, blending fully, one at a time. Add the flour and salt and mix until well combined. Pour the batter into the prepared pan. Bake for 25-30 minutes until the brownies are cooked through and set but not overbaked.
While the brownies are still warm, dollop the marshmallow crème over the top in large scoops and spread into an even layer.
In a medium saucepan or in a microwave-safe bowl in the microwave, melt the peanut butter and chocolate chips together over low heat, stirring constantly, until melted and smooth. Remove from the heat and stir in the rice krispies until evenly coated.
Scoop spoonfuls of the crispy topping over the marshmallow layer and gently spread into an even layer. Let the pan of brownies cool to room temperature and then refrigerate until the chocolate krispie topping is set, 1-2 hours. Serve chilled or at room temp.