Simmer the tomatillos and serrano in water until the tomatillos soften and turn olive green, about 8 minutes. Drain and blend with garlic, half the onion, half the cilantro, and 1 cup of the broth until smooth.

Cook bacon in a large pot over medium heat until crisp. Transfer to a plate, leaving about 1 tablespoon of the drippings in the pot.

Add the beef to the pot and cook, stirring, until browned and its juices release, about 5 to 7 minutes.

Pour in the tomatillo mixture and remaining 3 cups broth. Add salt and pepper; simmer gently for 15 minutes. Stir in the beans and simmer 5 minutes more until hot.

Stir in lime juice. Serve with bacon, the remaining chopped onion and cilantro, and sliced radishes.