Sauté the onions and garlic in olive oil. Heat the olive oil over medium heat in a large soup pot. Add the onions and sauté 2-3 minutes, then add the minced garlic and sauté 1-2 minutes more.
To the pot, add the split peas, ham bone with meat, bay leaf and broth. Bring mixture to a boil, then reduce the heat and simmer, covered, for 1 hour.
Remove the lid and stir, then remove the ham bone and chop or shred the meat into pieces.
Return the meat to the soup pot and add the carrots, celery, salt, pepper and thyme.
Simmer, uncovered, for an additional 30 minutes or until veggies are tender and soup is thickened.