Choo chee is a red curry reduced until it stops being a soup and becomes a sauce. Coconut cream is cooked hard until the oil splits out, the paste fries in that oil, and the whole thing thickens into something you spoon over rather than ladle around.
Prawns are the classic partner because they cook in ninety seconds and the sauce is already finished by the time they go in. Shredded kaffir lime leaf on top is not optional.