Mix potatoes, 2 containers chicken broth, jalapeno pepper, onion flakes, and minced garlic together in a large pot; bring to a boil and cook until the potatoes are softened, about 25 minutes.
Stir remaining carton chicken broth, cream, leeks, paprika, and dry onion soup mix into the mixture in the pot; continue cooking until thickened to your preferred consistency, about 20 minutes.