In a large mixing bowl, combine sour cream, cream cheese, sugar, milk, and vanilla. Beat with an electric mixer on high speed until smooth. Combine coffee and coffee liqueur.
Layer one package of the ladyfingers, cut side up, in a 2-quart rectangular baking dish. Brush with half of the coffee mixture. Spread with half of the cream cheese mixture. Repeat with remaining ladyfingers, coffee mixture, and cheese mixture.
Sprinkle with sifted cocoa powder. Cover and refrigerate for 4 to 24 hours. If desired, sprinkle serving plates with additional unsweetened cocoa powder. Cut dessert into squares to serve. Serves 15.