Preheat oven to 325 degrees F (165 degrees C). Grease and flour a 9x9 inch baking pan.
In a medium bowl, cream 1 1/4 cups of sugar and 4 tablespoons of butter. Add 2 eggs and mix well. Stir in 1/2 cup of the coffee liqueur. Sift together 1 cup of flour, cocoa powder, baking powder, and salt. Stir into the butter mixture until well blended. Spread half of this mixture evenly into the prepared baking pan.
In another bowl, stir together the 1/4 cup of flour and 1/4 cup of sugar. Add softened cream cheese and mix well. Stir in 1 egg, 2 tablespoons butter, and the vodka. Mix until smooth. Spread this evenly over the chocolate layer. Pour the remaining chocolate mixture over the top of this. You can make a pattern of stripes or swirl the chocolate with a toothpick.
Bake for 35 to 45 minutes in the preheated oven. When brownies are cool, brush with the remaining 1/4 cup of coffee liqueur.