In a large mixing bowl, combine warm milk, sugar, and yeast. Let sit until frothy, about 5 minutes.
Add melted butter, eggs, flour, and salt. Mix until a dough forms.
Knead the dough on a floured surface until smooth, about 10 minutes. Place in a greased bowl, cover, and let rise until doubled, about 1 hour.
Preheat oven to 375°F (190°C). Roll out dough into a rectangle. Spread softened butter over the dough, then sprinkle with brown sugar and cinnamon.
Roll up the dough tightly and shape it into a ring. Place on a baking sheet, cover, and let rise for another 30 minutes.
Bake for 25-30 minutes or until golden brown. Let cool completely.
Mix powdered sugar, milk, and vanilla extract to make the icing. Drizzle over the cooled cake and decorate with colored sugars.