Grapefruit and coriander cordial is an oleo-saccharum with the volume turned up. Sugar pulls the essential oil out of citrus peel by osmosis, no heat required; sealing the whole thing under vacuum for 24 hours makes that extraction more complete and keeps oxygen away from the oils while it happens. Coriander seed rides along in the same cure. It is the backbone of the Pa-Low-Ma.
Peel, Not Juice
Grapefruit juice is a difficult cocktail ingredient. It oxidises fast, it is inconsistent between fruit, and its bitterness is the sulphurous kind that turns unpleasant within a few hours of squeezing. Grapefruit peel is where the good bitterness lives — in the oil glands of the flavedo, the coloured outer layer — and that oil is aromatic, stable, and far more intense than the juice. Thirty grams of organic peel carries more grapefruit character than several times its weight in juice, and it keeps. Use organic fruit and wash it; you are extracting directly from the skin.
Why the Vacuum Bag
Sugar draws oil and water out of the peel by osmosis, and the process needs contact. In a vacuum bag the peel is pressed against the sugar with atmospheric pressure doing the work, so every surface is in contact for the whole 24 hours — and there is no air in the bag for the extracted oils to oxidise into. A sealed jar works and is what most people will use. It extracts slightly less and browns slightly more. Neither ruins the cordial; the bag is just better.
Crush the coriander seeds lightly first — just cracked, not ground. Whole seeds barely give anything up in a day; ground seed turns dusty and muddies the texture. Coriander and grapefruit share terpenes, which is why the pairing works and why gin botanicals so often put them together.
Two Acids and the MSG Question
Once the cure is done, the water goes in with 3 grams of malic and 6.5 grams of citric acid. Citric is the acid grapefruit actually tastes of and it carries most of the load; malic sits underneath and stops the sharpness from being one-dimensional. Together they take the cordial to roughly the acidity of fresh citrus juice, which is what lets a drink built on it read as a sour rather than as sweetened water.
The pinch of MSG is optional and I would take it. A few tenths of a gram is far below the threshold where anyone tastes it as itself; what it does is add glutamate, which broadens perceived body and makes a low-ABV drink feel less thin. The same reasoning as the MSG solution used elsewhere on this site. Leave it out and the cordial is still good, just narrower.