Preheat oven to 350° F. Lightly grease an 8-inch cake pan with butter.
Stir together sugar and cinnamon in a small bowl. Set aside.
Unroll crescent roll dough, and separate into 4 rectangles; pinch seams to seal.
Sprinkle cinnamon sugar mixture evenly over rectangles.
Starting with a long side roll up, jellyroll fashion. Press edges to seal.
Cut each log into 5 slices, and place, cut side up, in a lightly greased 9-inch round cake pan.
Bake at 350° for 30 - 35 minutes, or until golden and center is cooked. Remove from oven to cooling rack. Prepare glaze.
In a small bowl, combine powdered sugar, milk, and vanilla, stirring until smooth; drizzle over warm cinnamon rolls.