In a large mixing bowl, combine warm milk, sugar, and yeast. Let sit until frothy, about 5 minutes.
Add melted butter, eggs, and salt to the yeast mixture. Gradually add flour, mixing until a dough forms.
Knead the dough on a floured surface until smooth and elastic, about 10 minutes. Place in a greased bowl, cover, and let rise until doubled, about 1 hour.
Preheat oven to 375°F (190°C). Punch down dough and roll into a rectangle. Spread melted butter over the dough, then sprinkle with brown sugar and cinnamon.
Roll up the dough tightly and shape into a ring. Place on a baking sheet, cover, and let rise until doubled, about 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.