Prep the peas: Place split peas in a colander and rinse under cool water. Pick out any debris.
No soaking needed.
Sauté the aromatics: Warm the olive oil or butter in a large pot over medium heat. Add onion, carrots, and celery. Cook 5–7 minutes, stirring, until softened and lightly golden.
Add garlic and cook 30 seconds more.
Layer the flavor: Stir in the split peas, thyme, bay leaves, and a few grinds of black pepper. Let the peas toast for 1 minute to bring out their nuttiness.
Add liquid and ham: Nestle the ham bone or ham hock into the pot. Pour in the broth (start with 8 cups).
Bring to a gentle boil, then reduce to a simmer.
Simmer low and slow: Partially cover and simmer for 60–90 minutes, stirring occasionally. The peas should break down and the soup will thicken. Add a splash of water if it gets too thick before the peas are tender.
Shred the meat: Remove the ham bone or hock to a plate.
Pick off any tender meat, chop it, and return it to the pot. Discard skin, fat, and bones.
Adjust the texture: For a creamier soup, use an immersion blender to blend a portion right in the pot. Or scoop 2 cups into a blender, puree carefully, and stir back in.
Keep some chunks for body.
Season smartly: Taste before salting—ham and broth can be salty. Add salt as needed, more black pepper, and a small splash of apple cider vinegar to brighten the flavor if desired.
Finish and serve: Stir in diced leftover ham if you’re using it for extra heartiness. Ladle into bowls and top with chopped parsley.
Serve with crusty bread.