Place water, sweetpotatoes, cinnamon and salt in a saucepot set over high heat.
Bring water to a boil, reduce heat and simmer sweetpotatoes until tender (25 to 30 minutes)
Remove the pot from the heat and set aside. Cool sweetpotatoes in the cooking liquid to room temperature.
Remove the cinnamon stick from the pot.
Use an immersion blender or place sweetpotatoes and cooking liquid in a blender and process until ingredients are blended.
Place the mixture in the pot over low heat.
Stir in the brown sugar and milk.
Heat the mixture, stirring frequently, until it reaches a boil and has thickened, about 10 minutes.
Served warm in small mugs.