Heat Instant Pot to sauté. Add oil, onion, celery, carrot, and jalapeno and cook, stirring, until onions are translucent and soft, about 5 minutes. Add garlic, cumin, chili powder, and red pepper flakes and continue to cook, stirring, until fragrant, or about 1 minute.
Add black beans, broth, water, and bay leaf. Stir to combine, scraping bottom clean.
Place lid on Instant Pot and set on high pressure, Manual mode (or Pressure Cook, depending on model) for 45 minutes. Allow 13-15 minutes for it to come to pressure.
When cooking time has elapsed, let pressure release naturally for 15 minutes before turning vent to release any remaining pressure.
Remove bay leaf and discard. Remove about half of soup and use an immersion blender to blend (or a standard blender).
Stir blended soup and non-blended soup together, adding the cilantro and lime juice, and serve with desired toppings.
This soup if fairly thin immediately after cooking, but thickens up after cooling. If you want to eat this right away and prefer a thicker soup, reduce water by one cup. You can always add more, but it's harder to remove it once it's in.
If you prefer chunkier soup, omit step 5.
Like meat? Add diced ham, cooked bacon, or sausage to the soup.