Heat the olive oil over medium-low heat in a small saucepan. Add the onions, garlic, and jalapeño peppers and cook, stirring occasionally, until very soft, about ten minutes. Do not brown.
Transfer the cooked onion mixture to a blender or food processor and add the black beans, salt, cumin, lime juice, water, and cilantro. Blend until smooth, add more water or lime juice, little by little to thin it out (if needed). Taste and adjust seasoning.
Transfer dip to a serving bowl. Finish off with a drizzle of olive oil, a sprinkle of cheese, and cilantro. Serve with tortilla chips. Enjoy!