Set the Instant Pot to “Sauté” and add the butter to melt. Once melted, add the ham bone. Sear the ham bone on each side, approximately 1-2 minutes.
Add the onion and sauté until translucent. Add the minced garlic and cook for 30 seconds.
Season with thyme, rosemary, and add the bay leaves. Stir and cancel the sauté function on the pot.
Add the chicken stock, potatoes, and cooked ham to the pot. Season with the salt and pepper. Close and lock the lid, move the valve to “Sealing” and cook on high pressure for 10 minutes.
At the end of the cook cycle, do a controlled quick release to remove any remaining steam/pressure in the pot. Remove the ham bone and turn the pot to the sauté setting.
Pour in the half and half. To a glass measuring cup, combine the water and cornstarch. Mix well. Stir the cornstarch mixture into the soup. Stir frequently until the soup has thickened and reached a creamy consistency.
Add in the corn, stir to incorporate and warm through 1-2 minutes.
Season with salt and pepper, if needed. Garnish with cooked bacon, shredded cheddar cheese and freshly chopped thyme.