Cook the pasta soft. In a pot, combine the pasta with 3 cups of the water and 3 cups of the milk. Cook over medium heat for about 35 minutes, stirring now and then so it does not catch, until the pasta is very soft and the liquid has thickened.
Blend until silky. Tip the pasta mixture into a blender. Add the remaining 1 cup water, remaining 1 cup milk, one tin of condensed milk, the cinnamon, and the vanilla. Blend until completely smooth with no lumps. Take it further than you think you need to.
Chill. Refrigerate for at least 2 hours. Chicha is only right when it is properly cold.
Serve over lots of ice. Fill a glass with far more ice than feels reasonable. Pour the chicha over, drizzle condensed milk from your second tin, and finish with a sprinkle of ground cinnamon over the top.