Sterilize jars and set aside. Wash and trim the ridges of the starfruit (see video linked above), then slice thinly and remove seeds. If you prefer a smoother jam, roughly chop the slices before cooking.
Combine starfruit, sugar, and citrus juices, zest and ginger (if using) in a large non-reactive pot. Let sit for at least 1 hour (or overnight in the fridge) to draw out the juices and dissolve the sugar.
Bring to a gentle boil over medium heat. Stir frequently as the mixture thickens and the starfruit softens — about 45 minutes or until a food thermometer reads 220°F. If you reach this temperature, you will create a very thick/stiff jam.
Ladle the hot jam into sterilized jars, leaving ¼-inch headspace. Using a butter knife, run the knife along the edges of the jars to ensure no air pockets. Wipe rims clean, seal, and process in a boiling water bath for 10–15 minutes if storing long-term. Or, if not canning, allow the jars to cool and place directly in the refrigerator.