Add the vegetable broth, pizza sauce, black olives, pepperoni, green pepper, red onion, Italian seasoning, and salt to the Instant Pot. Stir gently to combine.
Secure the lid and set the pressure valve to sealing. Select high pressure and set the timer for 15 minutes.
When the cook time ends, carefully turn the valve to venting for a quick release of pressure. Remove the lid once the pin drops.
Ladle the hot soup into bowls and top each serving with shredded mozzarella cheese as desired.
Serve hot with fat head garlic breadsticks, if desired.