How to Make It
In a saucepan, combine 1/4 cup of the oil with the garlic and cook over moderate heat, stirring frequently, until golden, 4 minutes. Transfer the garlic oil to a blender. Add the rosemary, parsley, marjoram, salt, pepper, fennel, cumin, cardamom, vinegar and the remaining 3/4 cup of oil and puree until smooth.
Arrange the lamb chops in a shallow baking dish. Pour the marinade on top, turn to coat and refrigerate overnight. Return to room temperature before grilling.
In a small saucepan, heat the olive oil. Add the garlic and shallot and simmer over moderate heat until fragrant and softened, about 3 minutes. Transfer to a blender, add the lemon zest and let cool. Add the mint and a generous pinch of salt and pepper and puree to a chunky paste.
In a large skillet 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. Transfer the asparagus to a platter and drizzle with the mint dressing.
Light a grill. 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.