Rinse and sort split peas.
Heat oil in a pot; sauté onion, carrots, celery 5-7 min, garlic 1 min.
Add peas, ham, broth, bay leaf, thyme, salt, pepper, and potato. Boil, then simmer 1-1.5 hours.
Remove ham hock (if used), shred meat, and return to the pot.
Blend partially for smoothness, if desired. Taste and adjust the seasoning.
Serve in white ceramic bowls with parsley, croutons, bread, and cider.