Pick over the split peas, and remove any debris, if any.
Add bacon to a large soup pot or Dutch oven and cook over medium-low heat for 5-10 minutes, until most of the fat is rendered, but not crisp.
Add the olive oil, onion, celery and carrot to the pot. Season with salt and pepper, and cook 5 minutes, until slightly softened.
Add the fresh minced garlic, dried thyme, and Herbs de Provence. Stir well and cook 1 minute, until just fragrant.
Add the chicken stock, water, ham hock, bay leaves, and green split peas. Bring heat to high and bring to boil.
Once boiling, reduce heat to low, cover and cook for 2 hours, stirring occasionally every 5 to 10 minutes in the last half hour of cooking to prevent scorching.
After 2 hours, turn off heat and remove ham hock with tongs to a cutting board. Allow to cool slightly, then shred ham meat, and discard and excess fat and bones.
Remove bay leaves from the pot and discard. Add shredded ham to pot and stir. Season to taste with more salt and pepper, and serve.