In a large Dutch Oven, sauté the onions and garlic in the olive oil until soft and translucent. Season with the oregano, salt, and black pepper.
After 10-15 minutes, add the carrots, celery, potatoes, vegetable stock, and the first half of the split peas to the pot. Bring to a boil and simmer uncovered for 40 minutes. Be sure to stir often and skim the foam from the top as it rises.
After 40 minutes, add the remaining split peas and simmer for another 30 minutes. If you prefer a smooth soup as opposed to a chunkier one, use your immersion blender after 30 minutes to purée your soup. You can also pour into a blender, one cup at a time, careful of the hot soup. Return to the pot for the final addition of ham.
Add the diced ham to the pot, stir well to combine, and continue to cook for 10 more minutes.
Add salt and pepper, and serve it hot, hot, hot!
Notes
For reference, one pound of dry split peas equal about 5 cups of cooked split peas. Add half of the peas first and gauge how much room is left in your pot - if you have enough, add the full second half of the bag. If not, portion accordingly.