Heat olive oil in a large pot over medium heat until shimmering.
Add chopped onions, celery, and carrot with a sprinkle of salt. Cook, stirring occasionally, until softened, about 10–15 minutes.
Stir in minced garlic, ground cumin, and red pepper flakes. Cook until fragrant, about 30 seconds.
Pour in black beans and vegetable broth. Bring to a simmer over medium–high heat, then reduce heat to maintain a gentle simmer. Cook until beans are very tender, about 30 minutes.
Transfer about 4 cups of the soup to a blender, blend until smooth, then return to pot, or use an immersion blender to puree part of the soup in the pot.
Stir in chopped cilantro, vinegar or lime juice, and season with salt and pepper.
Serve hot, garnished with diced avocado, extra cilantro, radishes, or tortilla chips.