Over direct medium heat on the campfire or over medium heat on a camp stove or stovetop, heat the oil in a large Dutch oven.
Add the carrots, celery, and onion and sauté until softened, about 10 minutes.
Add the split peas and bay leaf, then nestle the ham bone in the pot. Pour the water over. It's ok if the ham bone is not fully covered.
Bring to a boil and skim off any scum that accumulates on top. Simmer gently, partially covered, until the peas have broken down and the soup is thick, about 1½ hours.
Remove the bay leaf and ham bone. Remove and shred or chop any meat from the ham bone. This should be easy to pull off with a fork.
Stir the meat from the bone along with the chopped ham into the soup. Simmer until heated through, 5 to 10 minutes. Thin with additional water, if needed. Season to taste with salt and pepper.