Melt butter in a large pot over medium-low heat. Stir in onion, celery, sliced garlic, chicken stock, water, ham, and bay leaf. Reduce heat and simmer for half an hour.
Stir in split peas, potatoes, and carrots. Simmer for about 1 hour and 15 minutes, stirring occasionally, until the soup is thick and the peas, potatoes, and carrots are tender. Season with salt and pepper to taste. Remove the bay leaf.
Notes
To STORE Split Pea and Ham soup leftovers, store them in the refrigerator for up to 5 days when kept in an airtight container. To FREEZE, place in your freezer for up to 3 months.To REHEAT, thaw in the fridge if frozen, then warm on the stove over medium heat until hot throughout. Stir occasionally to prevent sticking. If the soup has thickened excessively during storage, you might need to add a little water or chicken broth to regain the desired consistency before reheating. You can also reheat in the microwave until everything has warmed through.