Preheat the oven to 350 degrees F (175 degrees C).

Bring water and brown rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid is absorbed, 45 to 50 minutes.

Meanwhile, warm a large skillet over medium heat. Add beef, onion, and garlic to the hot skillet; cook and stir until meat is evenly browned and onion is softened, about 5 minutes. Set aside.

Remove and discard tops, seeds, and membranes of green, red, and yellow bell peppers. Arrange peppers in a baking dish with the hollowed sides facing upward. Slice the bottoms off peppers if necessary so that they stand upright.

Mix browned beef, cooked rice, 1 can tomato sauce, Worcestershire sauce, salt, and pepper in a bowl. Spoon mixture into each hollowed pepper. Mix remaining tomato sauce with Italian seasoning in a bowl; pour over peppers.

Bake in the preheated oven, basting with sauce every 15 minutes, until peppers are tender, about 1 hour. Sprinkle peppers with grated Parmesan cheese; serve warm.