Preheat the oven to 350°F. Arrange the bell pepper halves on a greased baking sheet, cut-side up. Cover with foil and bake for 15 minutes. After baking, discard any water collected inside the peppers.
While the peppers are baking, cook the ground beef in a large skillet over medium-high heat until browned. Drain excess grease.
Add the diced onion to the skillet and cook until softened, about 5 minutes. Stir in the taco seasoning, tomato paste, and minced garlic, and cook for an additional minute.
Pour in ¾ cup of water, bring the mixture to a boil, then reduce heat to medium-low. Simmer for 5 minutes.
Stir in the black beans and diced tomatoes with green chilies. Continue to simmer until the mixture is heated through, about 5 minutes.
Fill each baked pepper half with the beef mixture, then sprinkle shredded cheese on top.
Return the stuffed peppers to the oven and bake, uncovered, for 15 minutes or until the cheese is melted and bubbly.