In a saucepan, combine a third of the oil with the garlic and cook over a moderate heat, stirring frequently, until golden. Transfer the garlic oil to a blender. Add the rosemary, parsley, marjoram, salt, pepper, fennel, cumin, mint, vinegar and the remaining two thirds of oil and purée until smooth.
Arrange the lamb chops in a shallow baking dish. Pour the marinade on top, turn to coat and chill overnight. Return to room temperature before grilling.
Boil the potatoes in salted water for approximately 8-10 minutes until soft and tender. Drain and allow to cool slightly before slicing and leaving in a warm place.
In a pan of boiling salted water, cook the asparagus until crisp-tender, about 4 minutes. Drain the asparagus and run under cold water to cool; pat dry.
Remove the lamb chops from the marinade and grill over high heat, turning occasionally, until browned, about 10 minutes for medium-rare meat. Serve the lamb chops with the asparagus and sliced new potatoes.
See more Lamb recipes
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home and view the full Food safety at home video.