Rinse the split peas under cold water and pick out any small stones. Set them aside.
Place the ham bone in a large pot with the split peas, onion, carrots, celery, garlic, water, and bay leaf.
Bring the mixture to a boil over medium-high heat, then reduce to low and cover the pot.
Simmer for about 90 minutes, stirring now and then, until the peas are soft and the soup has thickened.
Remove the ham bone from the pot. Shred any remaining meat from the bone and return the meat to the soup.
Season with salt and black pepper. Discard the bay leaf.
Ladle the soup into bowls and serve with the crusty bread on the side.