In a large skillet over medium-high heat, heat oil. Add onion and cook, stirring occasionally, until softened and just starting to turn golden, about 5 minutes. Stir in garlic and tomato paste and cook, stirring, until fragrant, about 1 minute more. Add beef; season with salt and pepper. Cook, breaking up meat with a wooden spoon, until no longer pink, about 5 minutes. Drain excess fat, if needed.
Add tomatoes, Italian seasoning, and Worcestershire to beef mixture and cook, stirring, until liquid is slightly reduced, about 2 minutes. Remove from heat and stir in rice; season with salt and pepper. Keep warm.
Prepare a grill for medium heat; preheat 5 minutes. Cut tops off peppers and remove cores and seeds; reserve tops and discard cores and seeds. On a sheet tray, drizzle peppers and pepper tops with oil and rub to coat.
Grill peppers and pepper tops, covered and turning whole peppers occasionally and tops halfway through, until lightly charred and crisp tender, about 2 minutes per side for whole peppers and about 4 minutes per side for pepper tops.
Transfer pepper tops to a plate. Return peppers to sheet tray, arranging cut side up. Spoon beef mixture into each pepper. Generously pile cheese on top of beef mixture.
Arrange stuffed peppers next to each other, cheese side up, on grill, wrapping with foil but keeping cheese exposed if desired so peppers stay upright. Grill, covered, until cheese is melted, 8 to 10 minutes.
Arrange peppers and pepper tops on a platter. Top with parsley.
