Preheat and Prepare: Preheat the oven to 375°F (190°C). Unroll the crescent roll dough and arrange the triangles on a pizza pan, with the pointed ends toward the center to create a circular shape.
Form the Base: Overlap the edges of the triangles slightly and press the seams together to form a smooth pizza crust.
Add Butter and Cinnamon-Sugar: Brush the melted butter evenly over the dough. In a small bowl, mix the granulated sugar and cinnamon until combined. Sprinkle this mixture generously over the butter-coated dough.
Bake: Bake in the preheated oven for 12-15 minutes, or until the crust is golden brown and the cinnamon-sugar topping begins to caramelize.
Prepare the Glaze: While the pizza is baking, whisk together the powdered sugar, milk, and vanilla extract in a small bowl until smooth. Adjust the consistency by adding more milk or powdered sugar as needed.
Drizzle and Serve: Once baked, let the pizza cool for a few minutes. Drizzle the glaze over the top using a spoon or piping bag. Slice into wedges and serve warm.