Bring a large pot of water to a boil. Cook bell peppers in boiling water until softened, about 10 minutes. Arrange peppers in a baking dish with the cut side on the bottom of the dish.
Bake peppers in preheated oven for about 10 minutes. Remove from oven and set aside.
Heat oil in a skillet over medium heat. Cook and stir onion in hot oil until fragrant, about 2 minutes. Stir sofrito, garlic, salt, cumin, oregano, and black pepper with the onion; let mixture cook together for about 1 minute. Break ground beef into small pieces into the skillet; cook and stir until the beef is crumbly and completely browned, 7 to 10 minutes. Stir tomato sauce, capers, and rice through the beef mixture; spoon into the peppers. Sprinkle cheese over the top of the stuffed peppers.
Continue baking in oven until the cheese is melted, about 10 minutes.