Preheat your oven to 350°F (175°C).

In a medium saucepan over low heat, melt the unsalted butter. Stir occasionally until completely melted, then remove from heat.

In a large mixing bowl, combine the granulated sugar and brown sugar. Pour the warm melted butter over the sugars and mix until well blended.

Add the large eggs, one at a time, whisking well after each addition. Then drizzle in the vanilla extract.

In a separate bowl, whisk together the all-purpose flour, cocoa powder, and salt. Gradually incorporate this dry mix into the wet mixture, stirring until just combined.

Pour the brownie batter into a greased baking pan (9x13 inches). Spread it evenly and bake for 20-25 minutes, or until a toothpick inserted comes out with a few moist crumbs.

While the brownies cool, make the buttercream. In a bowl, beat softened unsalted butter until creamy. Gradually add powdered sugar, beating well. Pour in the Baileys Irish Cream and a splash of heavy cream, mixing until fluffy.

Once the brownies are completely cool, spread the Baileys buttercream evenly over the top.

Cut the brownies into squares. Serve immediately or chill slightly before serving.