Prepare the Dough: In a large bowl, combine warm milk with sugar. Sprinkle yeast over the milk mixture and let it sit for 5–10 minutes until bubbly. Add melted butter, vanilla extract, and salt. Stir to combine. Gradually add the flour, one cup at a time, until the dough begins to form. Knead for 5–7 minutes until smooth and elastic. Cover the bowl with a cloth and let the dough rise in a warm place for about 1 hour.
Prepare the Cinnamon Filling: In a small bowl, mix together brown sugar and cinnamon. Set aside.
Assemble the Buns: Once the dough has risen, punch it down and roll it out on a floured surface into a 12x8-inch rectangle. Brush the dough with melted butter and evenly sprinkle the cinnamon-sugar mixture over it. Roll the dough tightly from the long side and slice it into 12 equal pieces.
Bake the Buns: Place the cinnamon rolls into a greased 9x13-inch baking dish. Cover with a cloth and let them rise for 20–30 minutes. Preheat the oven to 350°F (175°C). Bake for 20–25 minutes, or until golden brown.
Prepare the Glaze: While the buns are baking, whisk together powdered sugar, milk, and vanilla extract in a small bowl. Add more milk if needed to reach your desired glaze consistency.
Glaze the Buns: Once the cinnamon rolls are done baking, drizzle the glaze over them while they are still warm. Serve immediately and enjoy!