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.
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