Start by cleaning and chopping your vegetables.
Get the ham hocks ready - dry them with a paper towel.
Get the ham bone ready if you have one to add.
Lay out the split peas on a sheet pan and pick out any inedible items that may have slipped into your bag - or any peas that don't look just right.
Put some olive oil into a big soup pot and warm the oil. Add the ham hocks and get a bit of a char on them - adding even more flavor to the pot / soup. Medium high heat for about 3-4 minutes per side. If you get a bit of fat or scum in the pot as a result of this step - go ahead and remove it before continuing on.
Take the browned ham hocks out of the pan.
Add more oil to the pan and saute your vegetables (onion, celery, carrots) for about 5-7 minutes. Add some S&P - building flavor layer by layer.
Add the garlic and cook for one or two minutes - as the garlic gets nice and fragrant.
Add the remainder of ingredients: broth, split peas, ham, ham hocks, ham bone, marjoram, bay leave, balance of S&P. Add enough water to cover your ingredients - or just about cover the ingredients. As you are bringing the soup up to boiling, skim off any scum that comes to the top. (I use a soup spoon and a bowl - skimming over the pot and then discard whatever I have in the bowl down the drain). Bring the soup to a Boil and then reduce to simmer with a mostly covered pot.
Simmer for as little as an hour - or as much as a couple of hours. Stir periodically, ensure you aren't boiling too aggressively and stir things around. After a bit - taste the soup. How is the seasoning? Now is the time to adjust.
When you are ready to eat - Pull out and discard the bay leaves, the ham hocks and the bone. Check the bone for any meat that is good to eat that you need to get off the bone. (Meat near the bone is generally more tender and succulent than that farther away) Add in / Add back any meat you've cut off the bone.
Serve !