Combine the paprika, garlic, cumin, salt, and cayenne in a small bowl.
Rub the seasoning mix all over the chicken breasts.
Heat the 2 TBSP of oil in a dutch oven or large pot over medium heat.
Add the chicken breasts to the dutch oven then place the lid on and cook, flipping occasionally, until browned on both sides and cooked through, 10 to 15 minutes (depending on how thick your chicken breasts are).
Set the chicken breasts aside for a few minutes to cool then refrigerate the chicken breasts in a covered container until ready to use.
SOUP:
Add the 3 TBSP of olive oil to the now empty dutch oven over medium-high heat.
Add the diced onion and green pepper to the dutch oven and cook, stirring often, for about 3 minutes.
Stir in the cornstarch, salt, paprika, garlic, and cumin and cook while stirring for about 1 minute.
Slowly stir in the water then use a wooden spoon or spatula to scrape any stuck on bits from the bottom of the pot.
Stir in the dried black beans and bring to a boil.
Place a lid on the dutch oven then reduce the heat to medium-low and simmer, stirring occasionally, until beans are tender, 1 1/2 to 2 hours.
Chop the chicken breasts into bite-size pieces then stir into the soup then simmer until heated through, about 2 more minutes.
Take the soup off the heat and stir in the lime juice and add salt & pepper to taste.
Ladle soup into bowls and top with any optional toppings.