Turn the Instant Pot to sauté mode and add olive oil. Once hot, add onions, carrots, and celery. Cook for 5 minutes until vegetables soften.
Add garlic and cook for 1 more minute until fragrant.
Turn off sauté mode. Add the rinsed split peas, diced ham, broth, bay leaves, thyme, salt, and pepper to the pot. Stir to combine.
Close the lid, set the valve to sealing, and cook on high pressure for 15 minutes.
When cooking is complete, allow the pressure to naturally release for 15 minutes, then do a quick release for any remaining pressure.
Open the lid and remove the bay leaves. Stir the soup well—it should be thick and creamy. If using a ham bone, remove it and shred any meat off before returning it to the soup.
Taste and adjust seasonings as needed. If the soup is too thick, add a bit more broth or water to reach your desired consistency.
Serve hot with crusty bread or crackers on the side.