Thoroughly sort through the dried split peas, removing debris, and rinse under cold water for about 2 minutes.

Soak the peas in water for 1 to 4 hours, then drain.

In a large Dutch oven, add split peas and 2.5 quarts of water, along with the ham bone, chopped onion, salt, pepper, thyme, and bay leaf.

Place the Dutch oven on medium-high heat and bring to a vigorous boil.

Reduce heat to low, cover and allow it to simmer for about 1.5 hours, stirring occasionally.

Remove the ham bone, dice the tender meat, and return it to the soup.

Stir in the chopped carrots and celery, then simmer uncovered for an additional 45 to 60 minutes.

Once thick and creamy, turn off the heat and discard the bay leaf before serving.