Preheat the oven to 375°. Line a 9-by-13-inch baking pan with foil or parchment paper, or grease and flour the pan.
For the filling: In a medium mixing bowl, beat the cream cheese until smooth. Gradually beat in the sugar. Add the vanilla and egg until just blended. Set aside.
For the brownies: In a bowl, whisk together the flour, cocoa powder and salt. Set aside.
In the top of a double boiler over simmering water, melt the butter, bittersweet chocolate and white chocolate chips, stirring until melted.
Remove from heat.
In a large mixing bowl, beat the eggs and sugar until light and fluffy, about 3 minutes. Add the melted chocolate mixture, beating until combined. Beat in the flour mixture and whisk in the beer; the batter will seem thin. Stir in the chocolate chips – they will sink to the bottom.
Pour the entire mixture into the prepared pan. Spoon the cream cheese mixture on top and run a knife through it several time to create a marble effect.
Bake 30 minutes, or until visible cream cheese is lightly browned and wooden pick inserted in the center comes out almost clean. Remove from the oven and cool in the pan before cutting into squares.
Please Note: Nutritional values listed may vary from final results depending on actual measurements and brands used to prepare the recipe.