Step 1
Heat the oven to 350 degrees. Spray a 9-inch loaf pan with nonstick spray, then dust with flour.
Step 2
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, brown sugar and granulated sugar on medium speed until light and fluffy, 4 to 5 minutes. Add the eggs one at a time, mixing on medium speed until incorporated, about 30 seconds each. Scrape down the sides of the bowl after each addition.
Step 3
In a medium bowl, whisk together the flour, baking powder and salt. Add the mixture to the bowl of the stand mixer and mix on low until incorporated, about 30 seconds. Add the Irish cream and mix on low to combine, 15 seconds more.
Step 4
Pour the batter into the prepared pan and spread in an even layer. Bake until the surface of the cake is lightly golden brown and a toothpick inserted into the thickest part comes out clean, 55 to 65 minutes. Let cool in the pan for 10 minutes, then unmold onto a wire rack to cool completely.
Step 5
Make the glaze: Whisk the powdered sugar and Irish cream together in a medium bowl to form a thick glaze. Spoon the glaze over the surface of the loaf, letting the excess drip down the sides. Let the glaze set for 10 to 15 minutes before slicing.