Add the olive oil, diced vegetables and salt and pepper to the dutch oven.
Sauté over medium high heat until fragrant, 3 to 5 minutes.
Add the ham hock and the dried split peas to the pot.
Add the broth (or water) and the bay leaves, and the thyme.
Bring to a boil.
Cover. Reduce to a medium-low simmer Let simmer for a minimum of 40 minutes to an hour. (I like to simmer until the ham is falling easily off the bone.)
Remove the ham hock from the soup mixture and pull the ham off the bone. Cut into bite sized pieces and returen the ham to the soup.
Adjust the thickness of the soup: If soup is too thick, add more broth or water until the desired consistency is reached. If the soup is too thin, let the soup simmer until some of the excess liquid is reduced.
Add salt and pepper to taste. Salt content will vary based on what type of broth you use.