Heat the olive oil in a large heavy pot over medium heat. Add the onion, celery, carrot and garlic, and cook until the vegetables are softened, about 5 minutes. Add the split peas, ham stock, water, bay leaf and ham. Bring to a boil, then reduce the heat to medium and cook until the peas are tender, about 1 hour. Season to taste with salt and black pepper. Remove the bay leaf before serving.
Makes 6 to 8 servings.