Add olive oil to Instant Pot® and select the “Sauté” function. Add garlic, carrots, celery, red onion, and crushed red pepper flakes then stir for a couple of minutes. Season with salt and black pepper, to taste.
Sauté everything in the large pot and stirring occasionally for 4-5 minutes. Do this until it's fragrant and the vegetables start to develop some color. Deglaze by adding the vegetable or chicken broth and scrapping any brown bits off the bottom of the pot. Press cancel.
Add sweet potatoes, bay leaves, and cherry tomatoes to the pot. Check to be sure seal is in place, the vent is turned to “Sealing” and set the “Manual” setting to 3 minutes.
When cook time is complete, allow pressure to naturally release for 10 minutes, then manually release any remaining pressure.
Remove lid and discard bay leaves and woody stems. Stir in fresh baby spinach or arugula and lime juice. Taste and adjust seasonings by adding additional salt and black pepper, if desired.
Ladle the soup into the bowls. Top the hot liquid with freshly shaved or grated Parmesan cheese and enjoy!