Set the Instant Pot to the Sauté setting and add the olive oil.
Add the garlic, carrots, celery, onion, and crushed red pepper flakes. Season lightly with salt and black pepper.
Cook for 4 to 5 minutes, stirring occasionally, until the vegetables begin to soften and become fragrant.
Pour in the broth and scrape the bottom of the pot to loosen any browned bits.
Press Cancel to stop the sauté function.
Add the sweet potato chunks, bay leaves, and tomatoes to the pot.
Secure the lid and ensure the pressure valve is set to Sealing.
Select the Manual or Pressure Cook setting and cook on high pressure for 3 minutes.
Once the cooking cycle ends, allow the pressure to release naturally for 10 minutes.
Carefully release any remaining pressure and remove the lid.
Discard the bay leaves.
Stir in the spinach or arugula and allow the greens to wilt in the hot soup.
Add the lime juice and stir well.
Taste and adjust the seasoning with additional salt and pepper if needed.
Ladle into serving bowls and top with freshly grated Parmesan cheese before serving.