How to Make It
Place onion in a medium-size heatproof glass bowl or jar, and set aside. Bring 1/2 cup water, vinegar, lemon juice, sugar, and salt to a simmer in a small saucepan over medium-high, whisking occasionally, until sugar dissolves. Remove from heat, and pour over onion, pressing onion to submerge in pickling liquid. Let cool; cover and chill until ready to use.
Place cumin seeds in a small skillet, and cook over medium, stirring often, until fragrant, about 2 minutes. Transfer to a plate; let cool 5 minutes. Place toasted cumin in a spice grinder or coffee grinder, and process until finely ground, about 15 seconds. Place ground cumin in a small bowl; stir in garlic oil, parsley, garlic, lime juice, smoked paprika, 1 tablespoon water, coriander, red pepper, salt, and honey. Taste and add more honey, if needed; set aside.
Preheat grill to high (450°F to 500°F). Toss together onions, 1 tablespoon garlic oil, and 1 teaspoon salt. Place onion wedges, cut sides down, on oiled grates; grill, covered, until deeply charred and blackened, about 5 minutes per side. Transfer to a medium bowl. Rub 1/4 cup chermoula all over lamb chops, and season with 2 1/4 teaspoons salt. Place lamb chops on oiled grates; grill, uncovered, turning occasionally, until a thermometer inserted in thickest portion of lamb registers 125°F, 10 to 12 minutes for medium-rare. Transfer to a large platter, and let rest 10 minutes.
While lamb chops rest, remove and discard blackened outer layer and root ends from onion wedges; separate wedges into petals. Toss together onion petals, remaining 1 teaspoon garlic oil, and remaining 1/4 teaspoon salt in a medium bowl. Top lamb chops with charred onion petals, 1/4 cup pickled red onions, chile slices, and purple basil. Spoon 1/2 cup chermoula over lamb chops. Serve with remaining chermoula and pickled red onions on the side.