Place the coffee in the distiller (see Resources) and distill completely. Ideally this should be very strong coffee. A French press will provide the strongest brew. Espresso, while it may seem like a good idea, will result in a very bitter product.
Reserve the resulting liquid in the refrigerator for up to 5 days.
Place 10 cylindrical glasses that have a diameter of 4cm/1.5in and are at least 5cm/2in tall on a flat surface. It is imperative that the glasses be straight and not tapered at the base in order to obtain an even cylinder. They should also have a flat bottom (not concave).
Combine the distilled coffee and sugar in a small sauce pot and whisk to dissolve the sugar. Adjust the sweetness as necessary. Stir the gellan gum and calcium lactate into the liquid while it is cold.
Bring to a boil to hydrate the gum and dissolve the calcium, and let boil for 5 seconds.
Remove from the heat and pour into the glasses, filling each one with about 60g/2.12oz. Refrigerate.
Once set, remove the jelly from the glasses very carefully. Reserve in the refrigerator and discard after 1 day.
Place the gelled coffee in a one-sixth pan with the pomegranate juice and soak for 1 hour.
Remove the gelled coffee from the juice and pat it dry with a clean paper towel.