Preparation
Preheat the oven to 350°F (175°C). Line an 8-inch square baking pan with parchment paper or coat it lightly with cooking spray. Set aside.
Streusel
In a medium mixing bowl, combine the brown sugar, cinnamon, and flour. Stir in the melted butter until the mixture is well-blended and crumbly. Set aside for later use.
Cake
In a medium bowl, sift together the flour, baking powder, baking soda, and salt. Set this dry mixture aside.
In a large mixing bowl, cream the softened butter, granulated sugar, and brown sugar using a stand mixer or hand mixer. Beat on medium speed until the mixture is light and fluffy, approximately 3 minutes. Use a rubber spatula to scrape down the sides of the bowl as needed.
Gradually add the eggs, one at a time, mixing well after each addition. Incorporate the vanilla extract and sour cream, ensuring all ingredients are evenly combined.
Reduce the mixer speed to low. Add half of the dry ingredients and mix briefly. Pour in the Irish cream liqueur and mix again for a few seconds. Add the remaining dry ingredients, blending just until the batter comes together—avoid overmixing. Scrape down the bowl as necessary.
Assembly
Spread half of the batter evenly into the prepared baking pan. Sprinkle half of the streusel mixture over the batter.
Layer the remaining batter on top, smoothing it gently with a spatula. Finish by sprinkling the remaining streusel mixture over the surface.
Bake in the preheated oven for approximately 40 minutes, or until a toothpick inserted into the center emerges clean. Allow the cake to cool in the pan on a wire rack for 15 minutes.
Glaze
In a small bowl, whisk together the sifted confectioners’ sugar and Irish cream liqueur until smooth. Drizzle the glaze over the cooled cake before serving.