Turn on the “Sauté” function on the pressure cooker. Heat 1 tablespoon olive oil in the pot, and when the oil shimmers add the onion, carrots, celery and garlic (as well as the diced ham or bacon, if using). Sauté just until the onion is translucent (about 6-7 minutes). Turn off the pot.
Add the ham hocks (or ham bone, if using), split peas, broth, bay leaf, thyme, oregano, basil and pepper.
Secure the lid on the pot. Close the pressure-release valve. Select “Manual” and set the pot at “High” pressure for 15 minutes. It may take the pot up to 15 minutes to come to pressure and start cooking.
At the end of the cooking time, allow the pot to sit undisturbed for 10 minutes, then release any remaining pressure.
Stir well to combine. Remove the bay leaf (and ham bone or ham hocks, if using). Chop up the meat from the ham hocks or bone, return the meat to the pot, and discard the bones and fatty pieces. Season with salt and pepper, to taste.
The soup will thicken as it cools, so thin with extra broth or water, if necessary.