Make the vinaigrette: lightly brush or spray the shallot all over with a bit of 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 let cool; remove and discard the peel.
Finely chop the shallot and put it in a medium bowl along with the remaining vinaigrette ingredients; whisk in the rest of the olive oil to create a smooth dressing.
Trim any excess fat from the lamb; let stand at room temperature 20-30 minutes before grilling.
Lightly brush or spray the lamb with oil and season with thyme, salt, and pepper.
Loosely cover the bones with 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 more for medium-rare.
Remove from the grill and let rest for 5 minutes before cutting into chops.