Place split peas, ham bone, carrots, onion, celery, thyme, bay leaf, salt, and pepper into a large pot; pour in water. Bring mixture to a boil and skim off any foam with a spoon. Reduce heat; place a lid on the pot slightly ajar to allow some evaporation. Simmer, stirring occasionally, until peas are tender and soup is thick, about 3 hours.
Remove ham bone from soup; strip meat from ham bone, chop meat, and return it to the pot.
You can substitute 2 smoked pork hocks or 1 small ham shank for the leftover ham bone.
Adjust thickness of soup by adding a little water to thin or remove broth with a spoon for a thicker soup.
I sometimes use an immersion blender for a quick second to blend the soup, making sure to leave some chunky peas, carrots, celery, and ham.
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