Beat egg yolks in the bowl of a double boiler until fluffy. Beat sugar into egg yolks until incorporated; beat in wine. Heat egg mixture over the double boiler until the cream thickens and small bubbles appear, about 5 minutes.
Stir the mascarpone cheese with a rubber spatula in a bowl until creamy. Pour egg mixture over the cheese; beat until filling is smooth.
Beat cream in a bowl with an electric mixer until soft peaks form; fold into cheese mixture.
Combine coffee-flavored liqueur and rum in a small bowl. Dunk enough cookies in the liquor to create a layer across the bottom of a baking pan; arrange cookies in the baking pan to create a cake base. Cover cookies with half of the filling. Dunk a second layer of cookies; arrange on the filling. Top with remaining filling; sprinkle with cocoa powder.
Place in the refrigerator until chilled, 3 to 4 hours.