Add the chopped carrots and celery. Continue to cook for another 2-3 minutes.
Add the rinsed split peas, ham bone, water/stock, thyme and bay leaves. Stir well.
Bring the soup to a boil and then reduce heat until simmering. Allow the soup to simmer covered, for 2 1/2 to 2 3/4 of an hour, stirring occasionally.
Remove ham bone. Chop all the meat off the bone, cut up to your desired size, and then add it back to the soup. Season the soup with salt and pepper to taste and let simmer for a few minutes more.
Notes
If using soup stock, choose a flavourful stock that isn't very salty. The ham will add plenty of salt and flavour on its own.