Rinse the black beans under cold water and sort through to remove any debris.
Set your Instant Pot to the 'Sauté' setting. Add a splash of water or a little oil.
Once heated, add the diced onion and cook for 3-4 minutes until translucent.
Stir in the minced garlic, diced bell pepper, and carrots, cooking for another 2 minutes.
Add the ground cumin, smoked paprika, and chili powder, stirring until fragrant (about 1 minute).
Cancel the 'Sauté' function. Add the rinsed black beans, vegetable broth (or water), diced tomatoes (with juices), and bay leaf. Stir well to combine.
Secure the lid on the Instant Pot and set the valve to the sealing position.
Cook on high pressure for 25 minutes. After the cooking time is complete, allow the pressure to release naturally for about 10-15 minutes, then carefully release any remaining pressure.
Open the lid and season the soup with salt and pepper to taste. Remove the bay leaf before serving.
Serve hot, garnished with fresh cilantro and lime wedges if desired.