Put the cutlets in a bowl with the oil, lemon juice, garlic and rosemary and toss well to combine. Cover and leave to marinate in the refrigerator for at least 1 hour or up to overnight.
Meanwhile, for the pesto, put the tomatoes, peppers, almonds, chilli and garlic in a food processor and process to a paste. Stir in the Parmesan and oil and season with salt.
Season the marinated cutlets with salt and pepper. Heat a ridged griddle pan over a high heat until smoking hot, or preheat a gas barbecue to high or, if using a charcoal barbecue, get the coals to the stage where there are no more flames and the coals are covered with a thin layer of grey ash. Add the cutlets and cook for 2–3 minutes on each side, depending on whether you like your lamb pink in the centre or well done. Serve with the red pesto on the side.