Pizza-Dough Cinnamon Rolls

Name: Pizza-Dough Cinnamon Rolls
Cuisine: American
Ingredients: Cinnamon Rolls; 1 stick unsalted butter, melted; 1 cup sugar; ¼ cup all-purpose flour; 2 tablespoons ground cinnamon; ½ teaspoon pure vanilla extract; 2 pounds prepared pizza dough; Egg Wash; 1 egg; 1 tablespoon water; Icing; 1 cup confectioners’ sugar; 3 tablespoons whole milk, or more as needed