Heat the olive oil in a large pot over medium-high heat. Cook the onion and bell pepper for 5 minutes, until softened at the edges.
Add the garlic, chili powder, cumin, and smoked paprika. Stir constantly for 1 minute until fragrant — blooming the spices in the oil is what deepens the flavor.
Pour in the tomatoes with their juice and the chicken broth. Add the torn corn tortillas and bring to a boil.
Reduce to a simmer and cook for 15 minutes, stirring occasionally. The tortillas will break down and thicken the broth.
For a smoother soup, pulse two or three times with an immersion blender. Leave it as is for a chunkier bowl.
Stir in the black beans, corn, and shredded chicken. Simmer for 3 to 4 minutes, just until everything is heated through.
Take the pot off the heat and stir in the lime juice and cilantro. Taste and add salt only if it needs it.
Serve topped with tortilla strips, diced avocado, shredded cheese, and a squeeze of lime.