Rinse and sort the split peas, removing any debris.
In a large pot, sauté the onion, carrots, and celery in a bit of oil over medium heat until softened.
Add the minced garlic and cook for another minute.
Stir in the split peas and ham hock.
Pour in the chicken broth and add the bay leaf.
Bring to a boil, then reduce heat to low.
Cover and simmer for about 1 hour, stirring occasionally.
Remove the ham hock and let it cool slightly.
Shred the ham from the bone and return it to the pot.
Season with salt and pepper, and discard the bay leaf before serving.