Set the oven rack about 6 inches from the heat source and preheat the oven's broiler.

Place pepper halves, skin-side up, on a baking sheet. Rub pepper halves all over with 1 tablespoon olive oil.

Broil in the preheated oven until browned and tender, about 10 minutes. Remove from the oven and reduce oven temperature to 350°F (175°C). Place peppers, skin-side down, in a baking dish.

Bring 1 cup water, rice, and beef bouillon cube to a boil in a medium saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 15 to 25 minutes.

Heat remaining 1 tablespoon olive oil in a large skillet over medium heat. Cook and stir onion and garlic in hot oil until onion is soft and translucent, about 10 minutes. Add ground beef, onion powder, garlic powder, and oregano to onion mixture; cook and stir until beef is browned and crumbly, 7 to 10 minutes.

Stir tomatoes, 1/2 of the Cheddar cheese, cooked rice, and Parmesan cheese into beef mixture until cheese is melted; remove from heat.

Whisk together ketchup, Worcestershire sauce, and remaining 1/4 cup water in a small bowl until well combined.

Assemble the stuffed peppers by placing a spoonful of ketchup mixture into the bottom of each pepper, adding a layer of rice mixture, spooning another spoonful of ketchup mixture over rice, topping with another layer of rice mixture, and sprinkling remaining Cheddar cheese over the tops.