Whisk together egg yolks and white sugar in a saucepan off heat until well blended. Whisk in evaporated milk and chocolate milk; place pan over medium heat. Stir constantly until boiling, about 5 minutes. Boil for 1 minute; remove from heat and cool slightly. Cover tightly with plastic wrap; chill in refrigerator for 1 hour.
Beat heavy cream, confectioners' sugar, and vanilla extract together in a bowl until stiff peaks form.
Remove yolk mixture from refrigerator; whisk in mascarpone until smooth.
Combine coffee, coconut-flavored rum, and coffee-flavored liqueur in a small bowl. Place ladyfingers in a bowl; drizzle coffee mixture over ladyfingers.
Arrange half of the soaked ladyfingers in the bottom of a 9x5-inch baking pan. Spread half the mascarpone mixture over ladyfingers, then half the whipped cream. Repeat with remaining ladyfingers and whipped cream; end with a layer of mascarpone mixture.
Sprinkle the tiramisu with cocoa powder and chocolate shavings. Cover with plastic wrap; refrigerate until set, 4 to 6 hours.
If you don't have mascarpone cheese, you can create a substitute by whipping 8 ounces softened cream cheese, 3 tablespoons sour cream, and 2 tablespoons heavy cream together until thick and smooth. Refrigerate until needed.
Per Serving: 462 calories;26.7 g fat;
47.4 g carbohydrates;
9.4 g protein;
291 mg cholesterol;
101 mg sodium.