Prepare canner, jars and lids. See The Ball Complete Book of Home Preserving for instruction and additional reference.
Place a saucer with 3 spoons on it in your freezer
Wash, pit and coarsely chop the plums
Put plums and sugar in a wide, 6-8 quart preserving pan or stainless steel saucepan.
Bring to a simmer, stirring frequently, then continue to cook for 5 minutes.
Pour into a colander set over a large bowl and stir the plums gently to drain off the juice.
Return the juice to the pan, along with ginger slices, cardamom and cinnamon and bring to a boil over high heat.
Boil, stirring occasionally until the syrup is reduced and thick, about 10 minutes.
Return the plum and any accumulated juice to the pan, along with the lime juice and bring to a simmer.
Simmer, stirring frequently, until a small dab of the jam spooned onto the cold plate and set in the freezer for a minute becomes somewhat firm (it will not gel), about 15 minutes.
Remove from heat.
Remove cinnamon sticks, ginger and (if using) bag with cardamom seeds.
Spoon your jam into hot jars, leaving 1/4 inch headspace.
Remove air bubbles and wipe rim.
Center lid on jar
Screw band down until resistance is met, then increase to fingertip tight.
Place jars in canner, making sure they are completely covered with water
Cover pot and bring to a boil
Boil for 10 minutes
Turn heat off, remove lid and let sit for 5 minutes
Carefully remove jars with jar lifter and place on a rack where they can be undisturbed for 24 hours.
Refrigerate any jars if their lids don't pop down.
Notes
This recipe assumes some knowledge of proper and safe canning techniques. Please see the Ball Complete Book of Home Preserving for guidance.