In a bowl, mix warm milk, sugar, and yeast. Let sit for 5 minutes until foamy.
Add flour, butter, egg, vanilla, salt, and cinnamon. Knead until smooth (8–10 minutes).
Place dough in a bowl, cover, and let rise for 1½–2 hours until doubled.
Roll dough into a 12×24-inch rectangle on a floured surface.
Spread softened butter over the dough. Sprinkle with brown sugar and cinnamon.
Roll tightly into a log and cut into 12 equal pieces.
Place rolls in a greased baking dish and let rise again for about 1 hour.
Preheat oven to 350°F (175°C) and bake for 20–25 minutes until lightly golden.
Mix glaze ingredients until smooth and creamy.
Spread glaze over warm rolls and serve.
