In a large bowl, mix warm milk, sugar, and yeast. Let it sit for 5 minutes until foamy.
Add melted butter, egg, and vanilla to the yeast mixture; stir until combined.
Gradually add flour and salt, mixing until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth.
Place dough in a greased bowl, cover, and let it rise for 1 hour or until doubled in size.
Roll out the dough into a rectangle about 1/4-inch thick.
Spread softened butter over the dough, then sprinkle with cinnamon and brown sugar.
Roll the dough tightly into a log and slice into 12 pieces.
Place rolls in a greased baking dish and let rise for another 30 minutes.
Bake in a preheated oven at 350°F (175°C) for 25-30 minutes until golden brown.