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Heat oven to 230C/fan 210C/gas 8. Season steaks, place a few basil leaves on each and split the mozzarella between them. Bring the sides of the steaks together to make an open parcel, securing the edges with a cocktail stick. If making up to a day ahead, cover and chill.
Heat a heavy-based roasting tin on a high heat, add the oil and brown the beef on all sides – this should take about 1 min in total and the meat will still be rare in the middle.
Add the peppers, their oil and the olives to the tin, pour over the vinegar, then roast for 2-3 mins for medium rare, longer for well done. Cover with foil and leave to rest for up to 5 mins. Scatter over remaining basil before serving.