Using a fine-mesh strainer lined with a coffee filter, a nut milk bag, or another similar very-fine straining device (I actually used a Chemex pour-over coffee drip, lined with a Chemex paper filter and it work great), gently pour out the cocktail and milk mixture to strain. It is critical that this process is done with care, as it is actually the milk curds that create a nest and filter the cocktail. This process will take a long time to drain. Do not stir. Let the curds and gravity do the work.