Warm the olive oil in your large pot over medium heat. Add the chopped onion and cook for about five minutes, stirring occasionally, until it turns soft and slightly golden. Stir in the garlic during the last minute so it doesn't burn.
Pour in two of the three cans of black beans along with the broth, salsa, cumin, salt, and pepper. Bring the mixture up to a gentle boil, then reduce the heat and let it simmer uncovered for about ten minutes so the flavors can meld.
Carefully transfer about half of the soup to a blender, or use an immersion blender right in the pot. Blend until smooth, then return it to the pot with the remaining whole beans still intact for texture.
Add the last can of black beans along with the lime juice, then stir everything together over low heat for another five minutes. Taste and adjust the seasoning, adding a splash more broth if the soup feels too thick.
Once everything is heated through, ladle the soup into bowls right away. This is the moment to add any spooky garnishes, since the soup is at its most cauldron-worthy while it's still steaming.