Use butter to grease the bottom of a jelly roll pan measuring 10 1/2x15 1/2 inches.
In a large mixing bowl, put the fudge brownie mix and add 1 cup of Irish cream liqueur, vegetable oil, and eggs. Use a beater to mix everything together until the batter is smooth.
Pour the batter into the prepared jelly roll pan.
Place the pan in the preheated oven and bake for around 20 minutes. To check if the brownies are cooked, insert a toothpick into the center of the pan; if it comes out clean, the brownies are done. Remove the pan from the oven and let it cool completely.
Take another large bowl and beat the unsalted butter until it becomes smooth. Add 5 tablespoons of Irish cream liqueur and beat the mixture until it becomes creamy.
Slowly beat in powdered sugar, one cup at a time, until the frosting reaches the desired stiffness.
Once the brownies are cooled completely, spread the frosting on top of them before serving.