Put the split peas in a bowl and cover with cold water for at least 20 minutes while you cook the vegetables.
Heat the oil in a large, heavy-bottomed pot over medium heat until hot but not smoking. Add the carrot, onion, and celery and season with salt, pepper, and a pinch of sugar. Cook, stirring, until the vegetables soften, 5 to 7 minutes. Add the garlic and cook for another 2 minutes.
Drain the split peas and add them to the pot. Add the bay leaf, marjoram, broth, and ham hocks. Give everything a good stir and bring the liquid to a boil over high heat, continuing to stir to keep the peas from scorching. Lower the heat, cover, and simmer for 1 hour. The peas will be partly disintegrated.
If the ham hocks aren't tender, leave them in. Otherwise use tongs or a slotted spoon to remove them from the pot and set them aside on a plate. Cook the soup for 30 minutes longer, or until the peas and other vegetables have completely broken down and the soup has thickened considerably. If it seems too thick, add more stock or water.
While the split pea soup is simmering, and as soon as the ham hocks have cooled enough to work with, use your hands to remove the meat from the bones, shredding it as you work. There won't be a lot of it, but what is there is very flavorful.
When the pea soup is done, use tongs or a spoon to remove and discard the bay leaf and marjoram sprigs. Taste and correct seasoning, bearing in mind that the bits of ham are salty. Add the reserved ham to the pot. If not serving immediately, let cool, cover, and refrigerate for a few days or freeze for up to 1 month. Reheat before proceeding.