Boil the Ham Bone (optional). Place your ham bone in a large soup pot and cover with enough water to fully submerge the ham bone. Cover pot and bring water to a boil over high heat. Once boiling, reduce heat to low and simmer for at least 1 hour (see notes).
Remove the Ham Bone and Strain Broth. After an hour or so, remove the ham bone from heat and strain the broth through a fine mesh strainer into a large, clean pot. Place the ham bone on a large plate and allow it to cool.
Cook the vegetables. Heat a large pot or Dutch oven over medium heat. Add olive oil and onions and mix to coat. Sauté for 3-4 minutes or just until the onions just start to soften. Mix in the chopped carrots and celery and sauté for an additional 8-10 minutes, stirring occasionally. Add the minced garlic and mix to combine.
Add the Split Peas. Add bay leaves, green split peas, thyme, salt and pepper. Add 10-12 cups of prepared broth, or mix of prepared broth plus low-sodium beef broth (see note below) and stir. Bring soup to a boil, reduce heat to a low and cover.
Add meat to the soup. As the soup cooks, cut off as much meat from the ham bone as possible and add to the pot. Add the bone to the pot, as well.
Simmer the soup. The longer the soup cooks, the better. That said, allow at least 2 hours for the soup to simmer and cook, stirring occasionally. After two hours, the soup should be thickening. Add more broth, as needed.
Serve. When ready to eat, season with additional salt and pepper to taste and discard bay leaves. Serve with croutons, if desired. Enjoy!