Heat your oven to 200°C/Fan 180°C/Gas 6. Trim the carrots. Cut them into quarters lengthways. Save a handful of the carrot tops.
Peel the onions and cut them into 4-6 chunks each. Place the carrots and onions on a baking tray, keeping the veg separate on the tray. Drizzle the carrots with 1 tbsp oil. Sprinkle the carrots and onions with salt. Drop on the unpeeled garlic clove. Slide into the oven and roast for 30 mins.
Drain and rinse the lentils. After the veg has cooked for 30 mins, remove the tray from the oven. Lift the onions and garlic off the tray.
Lower the oven to 160°C/Fan 140°C/Gas 3. Tip the lentils onto the tray with the carrots and toss together. Place back in the oven for 15 mins.
Place the soft, charred onions into a food
processor. Squeeze the roasted garlic from its skin into the processor. Whizz the onions and garlic till smooth. No processor? Chop the roasted onions and garlic as finely as you can and then crush with the back of a fork. Set aside.
Heat a frying pan for a few mins. When hot, drizzle in 1 tbsp oil. Place the lamb chops in the pan and cook for 3 mins on each side for rare. Cook a couple more mins for more well done chops. Place on a plate and cover with foil to rest.
Lower the heat under the pan. Add the butter with a pinch of cayenne pepper. Swirl together till the butter is melted.
Spoon the carrots and lentils onto a couple of plates. Top with a couple of lamb chops each. Dollop on some of the onion purée. Drizzle the spiced butter all over the chops and veg. Scatter over a pinch of chopped carrot leaves and serve.