Heat a large pot over medium heat. Add the ground beef, onion, and garlic. Cook until the beef browns and the onion softens, breaking up the meat as it cooks.
Stir in the minced chipotle peppers, adobo sauce, cumin, and chili powder. Cook for one minute until the spices smell fragrant.
Pour in the diced tomatoes with their juice and the beef broth. Add the black beans and stir to combine.
Bring the mixture to a boil, then reduce the heat to low. Simmer uncovered for 25 minutes, stirring occasionally, until the stew thickens slightly.
Taste and add salt and black pepper as needed. Remove from heat.
Ladle into bowls and top with chopped cilantro. Serve with lime wedges on the side.