Pizza-Dough Cinnamon Rolls

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