Warm the remaining olive oil in a large pot or Dutch oven over medium-high heat.
Add the onion and jalapeño and cook about 5 minutes, stirring now and then, until they start to soften. Stir in the garlic and cook another 1-2 minutes.
Pour in the broth, tomatoes with their juice, black beans, chicken, corn, lime juice, chili powder, cumin, salt, pepper, smoked paprika, and cayenne if using. Bring everything up to a boil.
Let it boil gently for 5-7 minutes — if the soup looks too thick or you want a brothier consistency, stir in a cup or two of water and adjust seasoning at the end.
Stir in the cilantro and let it boil for one more minute.
Taste and adjust the seasoning as needed, since saltiness can vary depending on your broth and beans.
Spoon into bowls, top generously with the crispy tortilla strips, and add avocado, cheese, or sour cream as desired. Serve right away.