Brazilian Burnt Eggs

Directions

1. 1
   In a pan, combine the water, sugar and cinnamon stick.
2. 2
   Bring to boil, uncovered, over medium-high heat.
3. 3
   Boil until thickened (like syrup).
4. 4
   To this syrup, add the eggs, stirring always, until the syrup dries up and the eggs burn a little.
5. 5
   Then pour the milk, slowly to moisten it.
6. 6
   When well blended, add butter.
7. 7
   Put in serving dish and sprinkle some powdered cinnamon over.