Step 1

Heat olive oil in a heavy soup pot or Dutch oven; cook and stir onion and garlic in the hot oil until soft, about 5 minutes. Stir herbes de Provence, turmeric, bay leaves, and cayenne pepper into the vegetables; cook and stir until fragrant, 2 to 3 minutes.

Step 2

Mix dried split peas, half the carrots, half the potatoes, vegetable stock, and water into vegetables and seasonings, bring to a bowl, and reduce heat to low. Cover pot and simmer until peas are nearly tender, about 35 minutes. Stir remaining half of carrots and potatoes and the ham into soup, cover, and simmer until vegetables are tender, about 25 more minutes.