In a large skillet bring hot dogs and brine to boiling; reduce heat. Simmer, uncovered, 10 minutes or until liquid is almost gone, turning hot dogs occasionally.
Meanwhile, in a large saucepan heat oil. Add onion, sweet pepper, and garlic; cook until tender. Add beans, cumin, and 1/4 tsp. salt. Cook and stir to heat through. Remove from heat; add vinegar. Using a potato masher, slightly mash beans. Top hot dogs in buns with bean mixture, radishes and cilantro.