Start by preparing the carrot puree; boil the carrots in a large saucepan of salted water until tender; usually 10-12 minutes. Drain and transfer to a food processor, then add the olive oil, butter and some seasoning. Pulse until it forms a thick puree. Transfer to a bowl and set to one side.
Pre-heat the oven to 210°.
Brush the lamb chops with the remaining olive oil and season well. Combine the breadcrumbs, parsley and seasoning in a large mixing bowl until combined. Sprinkle the breadcrumb mixture on both sides of the lamb chops, packing lightly to make them stick. Arrange on a lined baking tray and bake for 8-10 minutes, turning halfway through cooking.
Re-heat the puree in a saucepan over a low heat at the same time. Remove the lamb from the oven when ready and allow to rest for 3-5 minutes. Spoon the puree onto plates and arrange two chops alongside. Garnish with a sprig of oregano leaves and some freshly ground black pepper before serving.