In a large pot, sauté vegetables in a couple of tablespoons of olive oil, then add split peas.
Add water or stock to cover vegetables by about 2 or 3 inches (about 2 quarts).
Add vegetables, bay leaves, and thyme sprig and ham hock, if desired.
Reduce heat and simmer on low until peas are soft, about 45 minutes to an hour.
Remove the bay leaf and thyme sprigs and ham hock.
Use an immersion blender or regular blender and puree soup.
If using a ham bone, dice any ham and return back to soup.
Season to taste with salt and pepper
For slow-cooker, add all ingredients to slow-cooker and set to low for 6-8 hours. No need to sauté onions.