Preheat oven to 350°F (175°C) and grease a 9 × 9 inch baking pan with cooking spray.
In a medium bowl, whisk together brown sugar, cocoa powder, and espresso powder to prepare the filling.
In a large bowl, beat butter, granulated sugar, brown sugar, and baking powder with a handheld mixer until smooth and creamy.
Add eggs one at a time, beating well after each addition until fully incorporated.
Add milk, sour cream, and Baileys Irish Cream and mix until just combined.
Gradually add flour and beat until a smooth batter forms.
Pour half of the batter into the prepared baking dish and spread evenly.
Sprinkle the prepared filling mixture evenly over the batter layer.
Spread the remaining batter over the filling layer.
In a medium bowl, whisk granulated sugar, flour, cocoa powder, espresso powder, and salt for the topping.
Add melted butter and whisk until the mixture forms a crumbly topping.
Sprinkle the topping evenly over the batter.
Bake for 60–75 minutes until a tester inserted in the center comes out clean, covering with foil during the last 10–15 minutes if edges brown too quickly.
Drizzle melted chocolate over the cake.
Let the cake cool for 10–15 minutes before slicing and serving.
