Olive oil: 3 tablespoons， Onion, finely chopped: 1， Garlic, finely chopped: 2 cloves， Carrot, finely chopped: 1， Celery stalk, finely chopped: 1， Ham hock: 1 (1-1.5 pounds)， Chicken stock: 6 cups， Water: 2 quarts， Split peas: 1 pound， Fresh thyme: 2， Bay leaf: 1， Kosher salt and freshly ground black pepper: ， Extra virgin olive oil, for drizzling: ， Croutons, for garnish (optional):
1In a large heavy-bottomed saucepan, heat the olive oil over low to medium heat. Add the onion, garlic, carrot, and celery and cook until soft, 5 to 7 mins.
2Add the ham hock and toss to coat it with the oil and verges. Then add the stock, water split peas, thyme, and bay leaf. Bring to a boil, then reduce the heat to low and simmer, partially covered, for about 1 hour.
3Remove and discard the thyme and bay leaf. Remove the ham hock and set it aside.
4With an immersion blender, blitz the soup in the pot until smooth. Season with salt and pepper. Shred the meat from the ham hock and add it to the soup.
5Spoon into bowls and serve drizzled with a little extra virgin olive oil. Garnish with croutons, if you like.
If the ham hock isn't entirely submerged in the liquid, turn it every now and then so that it cooks evenly and doesn't dry out.