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Heat oven to 200C/180C fan/gas 6 and heat the oil in a large pan. Add the onion and cook for a few mins to soften. Add the garlic and beef, and cook until the meat is browned – break it up with a spoon as it cooks. Add the tomatoes, oregano, stock cube and ketchup. Season well, give everything a good stir and cover with a lid. Simmer for 30 mins.
Meanwhile, halve the peppers and scoop out the seeds and white membrane. Place cut-side up in a roasting tin, season and bake for 20 mins.
When the mince is cooked, divide it between the softened peppers. Return to the oven for 10 mins, sprinkled with cheese. Scatter with basil leaves before serving.