Heat olive oil in a large pot or Dutch oven over medium heat. Add onion, carrots, and celery and cook until softened, about 5-7 minutes.

Add split peas, chicken broth, ham hock (or diced ham), thyme, pepper, and red pepper flakes (if using). Bring to a boil, then reduce heat and simmer for 60 minutes, or until split peas are tender.

Remove ham hock and shred the meat. Return the meat to the soup. If using diced ham, skip this step.

Use an immersion blender to partially blend the soup to desired consistency. Alternatively, carefully transfer portions to a blender and blend until smooth, then return to the pot.

Season with salt and pepper to taste. Serve hot.