Preheat the oven to 350° F. Line a 9 by 13-inch baking pan with parchment paper (or spray with nonstick spray). Set aside.
In a large bowl, mix together the melted butter and sugar until smooth. Add the cocoa powder and stir to combine completely. Add the eggs, one at a time, and mix until smooth. Blend the vanilla and Irish Cream into the batter.
In a small bowl, whisk together the flour, baking powder, and salt and add this to the brownie batter. Stir until almost fully incorporate and then add the chocolate chips and finish stirring just until fully combined.
Pour into prepared pan and use a spatula to spread it evenly. Bake for 30 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs attached. Cool completely on a wire rack.
In a small bowl, mix together the butter and powdered sugar until creamy. Add the vanilla and Irish Cream and continue to beat until light and smooth.
Spread the buttercream onto the cooled brownies in the pan. Using an offset spatula makes this easier.
Chill brownies for at least one hour. Cut into squares while still cold, and serve brownies at room temperature.
Brownies can be frozen by placing them on a baking sheet until buttercream is completely firm. Wrap them well and freeze for up to 3 months. *In doing my research as to whether Irish Cream is gluten free, I've found that any gluten-containing ingredients in the whiskey used in Irish Cream has been removed through the distillation process. The National Institute of Health's Celiac Disease Awareness Campaign has stated that cocktails made with distilled alcohol are safe for celiacs to drink. Irish Cream has never affected me, and my sensitivity to gluten is extremely high. However, if you have problems with using Irish Cream, I would not suggest using it in these brownies. It can be left out completely and the brownies will still be amazing, or you can use another liqueur that you feel does not affect you.