Combine powdered sugar and cream cheese in a bowl; beat at high speed of a mixer until well-blended. Gently fold 1 cup whipped topping into cheese mixture.
Combine 1/2 cup sugar, 1/4 cup water, and egg whites in the top of a double boiler; place over simmering water. Beat at high speed of a mixer until stiff peaks form. Gently stir one-fourth of egg white mixture into cheese mixture. Gently fold in remaining egg white mixture; set aside.
Combine 1/2 cup hot water, 1 tablespoon sugar, espresso, and Kahlúa; stir well. Split ladyfingers in half lengthwise. Arrange 20 ladyfinger halves, cut sides up, in the bottom of an 8-inch square baking dish. Drizzle half of espresso mixture over ladyfinger halves. Spread half of cheese mixture over ladyfinger halves; repeat procedure with the remaining ladyfinger halves, espresso mixture, and cheese mixture. Spread 1/2 cup whipped topping evenly over cheese mixture; sprinkle with cocoa.
Place 1 toothpick in each corner and in center of Tiramisù to prevent plastic wrap from sticking to whipped topping; cover with plastic wrap. Chill 2 hours.