Heat a large pot or dutch oven over medium-high heat. Add the olive oil, diced onion, diced celery, and diced carrots. Saute for about 4 minutes or until vegetables have softened. Stir in the minced garlic and saute for an additional 30 seconds.
Add the split peas, ham hock, bay leaf, and chicken broth to the pot and gently stir.
Add a lid and bring the pot to a gentle boil. Once boiling, reduce the heat to medium-low and simmer for 1 hour. Give the soup a stir periodically and flip the ham hock over once or twice, while the soup is simmering, so that it gets even exposure to the hot liquid.
After 1 hour the peas should have completely broken down almost to a mush. If they are still retaining their shape, continue to simmer for 10 more minutes.
Next remove the ham hock from the pot and set it aside to cool. Add the diced potato to the soup and stir to combine. Continue to simmer for about 12 more minutes or until potatoes are tender.
While the potatoes are simmering, and once the ham hock is cool enough to handle, remove the meat from the bone and shred into small pieces.
Add the ham meat back to the pot with the soup and gently stir to combine.
Feel free to season the soup with salt and freshly cracked black pepper to taste. Enjoy with crackers, homemade croutons, or crusty bread!