Wash plums well and cut them in half to remove pits. Slice the plums into thin half moons and heap them into a low, wide pan.
Add the sugar and stir to combine. Cover the pan and let the plums macerate for at least an hour.
When the plums are quite juicy and most of the sugar has dissolved, remove the cover from the pan and place it on the stove.
Add the cardamom and lemon juice and bring the fruit to a boil.
Cook the fruit at a controlled boil, stirring regularly, for 30 to 40 minutes, until the plums soften and the syrup thickens. You’ll know when the jam is done because it will become more resistant to stirring, and when you pull the spoon out of the pan, the droplets will be thick and slow moving.
While the plums cook, prepare a boiling water bath canner and 8 half pint jars.
When the jam is done, remove the pan from the heat. Funnel it into the prepared jars.
Wipe the rims, apply the heated lids and clean rings, and process the closed jars in a boiling water bath canner for 10 minutes (do not start your timer until the pot returns to a full, rolling boil).
Once the time is up, remove the jars from the canner and set them on a folded kitchen towel to cool. The lids should seal promptly and will often make a pinging or popping sound as the vacuum forms. When the jars are sealed, the center of the lids will be concave and when pressed, the lid will not move or wiggle.