Make the Brownies: Preheat the oven to 350 degrees F. Grease a 9x13-inch pan.
In a medium saucepan, melt the unsweetened chocolate, butter and ¾ cup of the semisweet chocolate chips over medium heat. Stir occasionally while melting. Set aside and cool for 5 minutes.
In a large bowl, whisk the eggs thoroughly. Add the sugar and vanilla, and whisk until well blended. Stir the melted ingredients into the egg mixture, mixing well. Sift the flour, baking powder and salt into the mixture and stir well. Fold in the remaining ½ cup semisweet chocolate chips.
Pour the batter into the prepared pan, smoothing it into an even layer. Bake for 25 to 30 minutes, or until a toothpick inserted into the corner of of the pan comes out with moist crumbs.
Remove the brownies from the oven and immediately sprinkle the marshmallows over them. Return the pan to the oven for 3 more minutes.
Make the Crispy Chocolate Peanut Butter Layer: Meanwhile, place the milk chocolate chips, peanut butter, and tablespoon of butter in a medium saucepan. Melt over low heat, stirring constantly, until completely melted. Remove from heat, add the Rice Krispies and mix well. Allow to cool for 3 minutes.
Spread the mixture evenly over the marshmallow layer. Allow to cool to room temperature, then refrigerate for 30 minutes to make it easier to slice. The brownies can be stored at room temperature or in the refrigerator for up to 1 week.