1In large mixer bowl, cream butter and sugars til light and fluffy. (About 2 minutes.) Add eggs vanilla and kahlua, and mix well. In small bowl, whisk flour, cocoa and cream of tartar, then gradually add to creamed mixture, beating. Scrape bowl and beat again til well mixed. Stir in nuts. Spread half into greased 13x9 baking pan. (*I find that brownies bake best in METAL pans, not glass. Glass seems to dry out the edges too much. **You can also line your pan with foil first, then spray with butter-flavored cooking spray, and pour into that. It makes cutting the brownies later MUCH easier!)
For filling, combine ingredients and carefully spread over batter. Top with remaining batter. Bake at 350 for 40-45 minutes or til toothpick comes out clean. Don't overbake. Cool on wire rack.
For frosting, combine sugar, milk and butter in a saucepan, and cook and stir until sugar is dissolved. Add the marshmallows and chocolate chips, and cook and stir til melted. Remove from het and add vanilla. Cool til frosting reaches spreading consistency. (About 25 minutes.) Spread over cooled brownies. Cut into small bars. (4 dozen)