Preheat oven to 350 degrees. Line a 8x8 pan with foil, making sure to leave an overhang, for ease of removal.
In a medium saucepan melt butter and unsweetened chocolate over low heat, stirring constantly. Remove from heat and cool. Add sugar and then the eggs one by one, until just combined. Add vanilla.
In a small bowl, mix together the flour and baking soda. Add the flour mixture to the chocolate mixture.
Pour into the pan and bake for 30 minutes.
Let cool. Once cooled, frost with fudge frosting.
Fudge Frosting
In a microwave safe bowl, add chocolate chips, sweetened condensed milk and vanilla and microwave on high for 1 minute. Stir until smooth. You may need to microwave for an additional minute to get things all melted.
Once melted, add the Kahlua and pour over the top of the cooled brownies.