Preheat your oven to 350°F (175°C) and grease a 9×13 inch baking pan or line it with parchment paper.
Melt the unsalted butter in a medium saucepan over low heat. Stir in the granulated sugar, eggs, and vanilla extract until well combined.
In a separate bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt. Gradually add to the wet ingredients, stirring until just combined.
Fold in the Bailey’s Irish Cream gently into the brownie batter.
Pour the brownie batter into the prepared baking pan and bake for about 25-30 minutes. Check for doneness with a toothpick.
Allow the brownies to cool completely in the pan on a wire rack. Dust with powdered sugar before cutting into squares.