Add the vegetable stock and dried split peas to a large pot. Bring to a boil for 2 minutes. Turn off the heat and let soak for an hour.
While the peas are soaking, dice the shallot, carrots, and potato and mince the garlic. If you are not using pre-diced ham, you'll need to finely dice that, as well.
About 15 minutes before the peas are done soaking, add the olive oil to a large skillet over medium heat. Add the shallot and garlic and cook for 2-3 minutes, until just soft. Mix in the ham and thyme and cook for an additional 2-3 minutes.
Add the ham mixture to the pot with the peas and season with salt and pepper. Turn the heat back on to high and bring to a boil. Reduce heat and simmer for an hour, or until the peas are tender.
Add the carrots and potatoes to the pot and cook until the potatoes are just fork tender, about 30 minutes.
Serve hot. Top with additional ham and black pepper, if desired.
nutritional information is given as an estimate only and may vary