Wash the plums, halve them, and remove the pits. Spread them in a large roasting tray and scatter the brown sugar over the top. If you have time, let them sit for 30 minutes to start drawing out the juices.
Heat the oven to 180°C (350°F). Bake the plums uncovered, so they release their juice and slowly reduce.
After about 1½ to 2 hours, lower the oven to 160°C (325°F) and keep baking, until the jam is thick, dark, and glossy - about 2½ to 3 hours in total. For a smooth, magiun-style spread, blend it with a stick blender; leave it as is for a rustic jam.
Stir in the rum and bake for 15 more minutes so the aroma settles in. Fold in the toasted walnuts right at the end so they stay crunchy.
Test the set on a cold plate: drop on a little jam, wait a minute, then push it with your finger. If it wrinkles, it is ready.
Ladle the hot jam into clean, sterilized jars, seal, and let cool. Store sealed jars in a cool, dark place; refrigerate once opened.