Preheat waffle iron to 350 degrees F. Combine flour, sugar, cocoa, dry yeast and salt in a large mixer bowl and stir until blended.
Place milk, water and butter in a microwave-safe bowl. Microwave on HIGH in 15 second increments until very warm but not hot to the touch (120° to 130°F. Butter won’t melt completely).
Add milk mixture to flour mixture, along with red food coloring and egg. Mix for 2 minutes at medium speed of stand mixer with dough hook attached, scraping bowl occasionally. Dough will form into a ball. Continue mixing for 5 minutes on medium speed.
Transfer dough to a lightly floured countertop and press out to 1/2 inch thick rectangle, about 9×13 inches. Cut into 8 equal parts and press each part into a round.
Place each dough round into waffle maker and cook for 1 minute, until cooked through. Remove and continue with remaining dough rounds. Place onto serving plate.
Combine all frosting ingredients (start with 1 tablespoon milk and add more if needed) in a large bowl and beat until creamy. Drizzle over waffle rolls to serve.