Begin by setting the Instant Pot to "Sauté" mode and adding the olive oil. Once the pot is heated, sauté the diced onion and celery for 2-3 minutes until softened.
Incorporate the minced garlic and diced ham, continuing to sauté for another 2-3 minutes to enhance the flavors.
Add the vegetable broth, cubed Yukon Gold potatoes, thyme, and rosemary to the pot. Stir well to combine all the ingredients.
Lock the lid in place and set the vent to sealing. Cook the mixture on high pressure for 5 minutes.
After cooking, allow a natural pressure release for 10 minutes, then carefully release any remaining pressure. Open the Instant Pot lid.
Stir in the heavy cream, and season with salt and pepper to taste.
For a creamier, thicker consistency, mash some of the potatoes directly into the soup.
If desired, create a cornstarch slurry by mixing cornstarch with water, and add this to the soup while on sauté mode. Let it simmer for 3-4 minutes to thicken the soup.
Notes
If using low-sodium broth, be sure to add between 1/2 to 1 teaspoon of salt, as needed. Regular broth may not require additional seasoning.
Yukon Gold potatoes are recommended for their ability to retain their shape and creaminess in the soup, but russet potatoes can also be used as an alternative.
To achieve a thicker soup, a cornstarch slurry can be added during the final stages of cooking for an extra creamy texture.