Place the butter in a 6-quart Instant Pot and press Sauté. Once melted, add the onions, garlic, basil, and oregano and cook for 4 minutes or until the onions are soft. Press Cancel to stop the Sauté.
Add the cream cheese and use a whisk to loosen or you will get clumps. Slowly whisk in the broth. Add the tomatoes, parmesan, salt, and pepper.
Seal the lid, press Pressure Cook or Manual, and set the timer for 8 minutes. Once finished, turn the valve to venting for a quick release.
Remove the lid and puree the soup with a stick blender; or transfer the soup to a regular blender or food processor and process until pureed.
Season with additional salt and pepper, if desired. Ladle the soup into bowls and garnish with more parmesan and basil leaves.