Preheat the oven to 350 degrees F. Adjust racks to the center of the oven. Spray a Bundt cake pan very well with nonstick spray.
Add the butter to a saucepan over medium heat. Once gently simmering, whisk in the cocoa, espresso and beer until blended and the butter is melted. Set aside to cool while you prepare the remaining ingredients.
Add the sugars, eggs, cream cheese and vanilla to a large bowl and beat together using a hand mixer until fluffy, about 4 minutes.
Whisk the flour, baking soda and baking powder together in a medium bowl.
Slowly beat in the cooled cocoa mixture to the egg and sugar mixture. Beat until incorporated, and then add the dry ingredients in increments of three, and continue beating until blended.
Add the batter to the prepared pan and bake until a toothpick inserted into the center of the cake comes out clean, about 45 minutes. Let cool completely before removing from the pan. Serve with caramel sauce.