Sort and rinse the dried green split peas under cool running water. Place them in a Dutch oven and cover with water.

Bring the pot to a boil for 2 minutes, then remove from heat and let the peas soak for 1 to 4 hours. Drain the soaking water.

In the same Dutch oven, add the drained split peas and ham bone, followed by the chopped onion, salt, pepper, thyme, and bay leaf.

Pour in 2-½ quarts of fresh water and bring to a rolling boil.

Reduce heat to a gentle simmer, cover, and cook for about 1-½ hours, stirring occasionally.

Carefully remove the ham bone, shred and dice the ham, then return to the pot and stir.

Add chopped carrot and celery to the pot, simmer uncovered for an additional 45 minutes to 1 hour.