Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the diced onion, garlic, and carrot to the pot. Sauté for about 5 minutes, or until the onion becomes translucent and the garlic is fragrant.
Stir in the diced celery and potatoes. Continue to cook for an additional 3 minutes.
Stir in the diced tomatoes and tomato paste. Mix well to combine.
Pour in the chicken broth and water, stirring to incorporate all the ingredients.
Add the bay leaf, smoked paprika, oregano, and salt and pepper to taste. Stir everything together.
Increase the heat to medium-high and bring the soup to a boil.
Once boiling, reduce the heat to low and allow the soup to simmer, uncovered, for about 45 minutes to 1 hour.
Taste the soup and adjust the seasoning with more salt, pepper, or smoked paprika if desired.
Stir in the kidney beans and white beans. Let them heat through for about 10 minutes.
Add the chopped cooked chicken to the soup and continue simmering for another 10-15 minutes.
Before serving, remove the bay leaf from the soup.
Ladle the soup into bowls and garnish with freshly chopped parsley or cilantro. Serve with lemon wedges on the side.