To make the vinaigrette: Lightly brush or spray the shallot all over with a bit of the olive oil. GRill over Direct Medium heat until it is blackened in spots and very soft throughout, about 15 minutes, turning once. Remove the shallot from the grill and allow to cool. Remove and discard the peel. Finely chop the shallot and put it in a medium bowl along with the remaining vinaigrette ingredients, whisking in the rest of the olive oil to create a smooth dressing.
Trim any excess fat from the lamb. Allow to stand at room temperature 20 to 30 minutes before grilling. Lightly brush or spray the lamb with oil and season with the thyme, salt, and pepper.
Loosely cover the bones with aluminum foil to keep them from burning. Sear, bone side down first, over Direct Medium heat until lightly browned, 2-4 minutes, turning once (flare-ups might occur).
Move the lamb over Indirect Medium heat and grill to desired doneness, about 15 minutes for medium-rare. Remove from the grill and let rest for 5 minutes before cutting into chops. Serve warm with vinaigrette.