Cook the jackfruit in a little water until it is very soft. Allow to cool and pulse just once or twice to get a mostly smooth paste with still some texture.
Put jackfruit paste and jaggery syrup (or sugar) in a heavy-bottomed pan and cook on medium heat. Make sure you taste for sweetness at the outset and adjust by adding more sugar or jaggery syrup if the fruit wasn't sweet enough to complement the sweeteners.
Continue cooking on medium heat. Midway, the mixture will thicken and boil like volcanic mudpots—you will have to stir constantly to keep mini explosions from happening and messing your cooking area. Stirring keeps the boil at bay.
After a while, when most of the water has evaporated, the boil will subside. Add 1-2 teaspoons of ghee to keep the mixture from catching at the bottom.
Now add the coconut milk, a cup at a time and continue mixing and cooking. The mixture will have liquified but will quickly thicken again.
Once it thickens a second time, add again 1-2 teaspoons of ghee. Continue to cook until the mixture becomes glossy and very thick. Switch off the flame.
In a small tempering pan, add the remainder of the ½ cup ghee—yes, all of it—and heat. Fry the coconut bits in this, and tip this into the hot jackfruit jam.
Turn on the flame again to medium and cook until glossy and with a halva-like jiggle, about 7-8 minutes. Switch off the flame.
Add the flavorings.
Bottle in clean, dry jars, cool and store, refrigerated.
This jam is a much-thickened version of chakka pradhaman. Save the coconut milk addition for the very end and do not thicken as much, and you have a pradhaman instead of a halva/jam.