Heat the olive oil in a large, heavy pot (about 4-6 quarts) over medium heat.
Add the onion, celery, and carrots, and cook until the onions are soft.
Add the bay leaves, dried thyme, and season with salt and pepper.
Add the rinsed split peas and stir to combine.
Add the broth and the ham/ham bone and bring to a boil.
Turn heat down to low, cover, and simmer for 1 hour.
Check on the soup, stirring every 20-30 minutes.
The soup is ready when the peas are soft, about 1 to 1 ½ hours of cooking time.
Using tongs, remove the ham onto a cutting board and let cool slightly.
Remove the meat from the bones, chop, and stir back into the soup (discard the bones and skin).
Taste and season with salt and pepper as needed.
Remove the bay leaves.
Use a stick blender or regular blender (work in small batches) to puree soup to desired consistency.
