Start Cooking Vegetables: Heat the olive oil in a large Dutch oven or soup pot over medium heat until shimmering. Add the onions, celery, and carrot, and a light sprinkle of salt. Cook, stirring occasionally, until the vegetables are soft, about 10 to 15 minutes.
Add Spices and Liquids: Stir in the garlic, cumin, and red pepper flakes and cook until fragrant, about 30 seconds. Pour in the beans and broth and bring to a simmer over medium-high heat. Cook, reducing heat as necessary to maintain a gentle simmer, until the broth is flavorful and the beans are very tender, about 30 minutes.
Blend the Soup: Use an immersion blender to blend the soup.
Final Touches: Stir in the cilantro, vinegar/lime juice, and salt and pepper to taste.