Heat the oil in a large stockpot over medium heat. Add the onion and red peppers and sauté for 5 minutes, or until the onion begins to soften.
Next, add the garlic, cumin, paprika, salt, and cayenne. Decrease the heat to medium-low and sauté for 2 minutes, or until the spices are wafting a rich, toasted scent, stirring frequently.
Stir in the black beans and vegetable broth. Increase the heat to medium-high and bring to a rolling boil. Reduce the heat to medium-low or as needed to maintain a steady gentle simmer until the beans are very tender, about 20 to 25 minutes.
Turn off the heat and transfer about 3 cups to a high-speed blender. Securely fasten the blender lid and place your hand and a kitchen towel on top to ensure the top stays in place. Carefully blend until smooth.
Return the blended soup to the pot and stir to incorporate. Stir in the cilantro and lime juice. Taste and season with more sea salt to taste (I usually add another 1 teaspoon—you may need to add even more if you used low-sodium stock/broth).
Ladle into bowls, top as desired, and serve.
Leftovers will keep for up to 5 days in the refrigerator and up to 1 month in the freezer.