1. Wash the plums under cold running water and pat them dry with paper towels. Then cut them in half and pry out the pits. With a nutcracker or the tip of a knife, break open 12 of the pits and remove their kernels.
2. Combine the plum halves and the 12 kernels in a 6- to 8-quart pot. Stir in the sugar. Let the mixture rest at room temperature for 30 minutes, then set the pot over low heat and cook, stirring constantly with a wooden spoon, until the sugar dissolves.
3. Bring to a boil over high heat, reduce the heat to moderate, and cook, stirring occasionally, for 45 minutes, or until the jam thickens and reaches a temperature of 221° (or 9° above the boiling point of water in your locality) on a jelly, candy or deep-frying thermometer.
4. Remove from the heat. With a large spoon, carefully skim off the foam from the surface and ladle the jam into hot sterilized jars or jelly glasses.
