Place the quinces in a saucepan and cover with cold water. Bring to the boil, then reduce the heat and simmer for 30 minutes or until soft. Drain and leave to cool. When cool enough to handle, cut each quince in half and remove the core, then peel and place in a large bowl.
Mash to a smooth purée, then stir in the garlic, 3 tablespoons of the oil and the mayonnaise until well combined. Season with salt and pepper.
Rub the remaining oil over the lamb and season well. Heat a griddle pan until smoking hot, then add the lamb and cook for 5–7 minutes on each side until charred and just pink in the centre. Serve with the quince aioli scattered with chopped parsley.