Add your Rum, Chai syrup and lime juice into a container and stir to combine.
Stir the mix into the milk, and let the mix rest for a few minutes, until it starts to separate.
Filter the mix through a coffee filter, but do not remove the curds, as they help with clarification. When you notice the rate of liquid slowing down, transfer the curd-filled coffee filter over to a clean container. Add the contents from the first pass back to the top of the filter and top it up until it's completely passed through (this can take quite a long time).
Serve your clear cocktail over a single large ice cube and garnish with a whole star anise.