In large bowl, with electric mixer, beat egg yolks with sugar until thick. Fold in mascarpone cheese by hand. Stir in 1/2 cup Kahlua. In another bowl beat egg whites until stiff peaks form. Fold into the mascarpone mixture. Combine 2 cups coffee and remaining 2 tablespoons Kahlua in a shallow pan. Dip half of the ladyfingers into the coffee mixture and arrange in a single layer in a 9-by-13-inch baking dish. Spoon half of the mascarpone cheese mixture over the ladyfingers and spread evenly. Sift half of the cocoa over the cheese. Dip the remaining ladyfingers in coffee mixture and arrange over the cocoa. Spread remaining mascarpone cheese mixture over the ladyfingers and sift remaining cocoa over all. Refrigerate for at least 3 hours before serving. Heat remaining 1/4 cup coffee and 1/4 cup chocolate chips in a small sauce pan. Stir until smooth. Cool slightly and drizzle over the Tiramisu to serve.
