Place the garbanzo beans, white beans, bulgur, and raisins in separate bowls and add water to cover.
Let stand overnight.
The next day, combine the garbanzo beans and white beans in a saucepan with water to cover. Bring the water to a boil; reduce heat to low and simmer, covered, until the beans are tender, 1 to 1 1/2 hours.
Drain the wheat and transfer it to a large saucepan.
Add the 15 cups water (3 quarts plus 3 cups) and bring to a boil. Reduce the heat to low and simmer until tender, about 15 minutes, skimming and discarding any foam that appears.
When the wheat has thickened, stir in the sugar and bring the mixture to a boil.
Drain the cooked beans and add them to the wheat mixture. Stir in the raisins, apricots, orange peel, and cloves. Reduce the heat and simmer until the mixture thickens and the fruit is tender, about 15 minutes.
Pour the pudding into individual serving bowls.
Garnish with toasted sesame seeds, chopped walnuts, chopped pistachios, currants, and cinnamon. Allow the pudding to cool and then serve.
