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.