In a large pot, heat the olive oil over medium heat. Add the chopped onion and garlic, and sauté until the onion is translucent, about 5 minutes.
Add the diced carrots and celery to the pot, cooking for an additional 5 minutes until softened.
Stir in the dried split peas, thyme, bay leaf, and chicken broth. Bring the mixture to a boil.
Reduce the heat to low, cover, and let simmer for about 1 hour, or until the peas are tender. Stir occasionally to prevent sticking.
Once the peas are tender, add the diced ham to the pot and cook for another 10 minutes to heat through.
Remove the bay leaf, and season the soup with salt and pepper to taste.
Serve hot, garnished with fresh parsley.