Prepare the Dough. In a bowl, combine warm milk and sugar. Sprinkle yeast over the mixture and let it sit for 5-10 minutes until frothy. In a large bowl, whisk together flour and salt. Make a well in the center and add the yeast mixture, melted butter, eggs, and vanilla extract. Mix until a dough forms, then knead on a floured surface until smooth and elastic. Place the dough in a greased bowl, cover, and let it rise until doubled in size.
Assemble the Star Bread. Divide the dough into four equal parts. Roll each part into a 10-inch circle. Place one circle on a parchment-lined baking sheet. Spread a thin layer of softened butter and sprinkle cinnamon-sugar over it. Repeat the process, stacking each circle with butter and cinnamon-sugar. Place the final circle on top. Using a small round object, place it in the center of the dough stack. Make eight equally spaced cuts from the edge to the center, creating sixteen sections. Take two adjacent sections and twist them away from each other. Pinch the ends to seal. Repeat with the remaining sections. You should finish with 8 twisted points. Let the assembled bread rise for 15-20 minutes.
Bake the Star Bread. Preheat the oven to 375°F. Bake the Star Bread for 20-25 minutes or until golden brown. Allow it to cool on the baking sheet for 10 minutes, then transfer it to a wire rack to cool completely.
Make the Glaze. Whisk together powdered sugar, milk, and vanilla extract until smooth. Drizzle the glaze over the cooled Star Bread.
Serve and Enjoy. Place the Star Bread on a festive serving platter. Invite everyone to tear off a piece and enjoy the layers of cinnamon-sugar goodness.