How to Make It
Combine garlic, shallots, chopped parsley, 1/4 cup oil, and thyme leaves in a food processor; process until mixture forms a paste, about 2 minutes. Slather paste evenly over lamb. Cover lamb, and refrigerate at least 6 hours or up to 8 hours or overnight. Remove lamb from refrigerator; let stand at room temperature 30 minutes.
Preheat a gas grill to very high (500°F and up) on one side, or push hot coals to one side of a charcoal grill. Sprinkle lamb racks evenly with 41/2 teaspoons salt and 11/2 teaspoons pepper. Wrap lamb bones with aluminum foil. Place lamb, fat cap sides down, on oiled grates over lit side of grill. Grill, covered, until lamb is browned, about 5 minutes. Flip lamb, and move to oiled grates on unlit side of grill. Grill, covered, to desired degree of doneness, or until a thermometer inserted in thickest portion of meat registers 124°F for medium-rare, about 20 minutes, flipping lamb halfway through cook time. Remove from grill; let cool 10 minutes.
Cut squash, zucchini, and onions into 3/4-inch pieces; leave tomatoes whole. Toss together vegetables, remaining 2 tablespoons oil, remaining 1 1/2 teaspoons salt, and remaining 1/2 teaspoon pepper. Place on oiled grates over lit side of grill; grill, covered, until just tender and slightly charred, about 5 minutes, flipping once. Remove from heat. Toss together grilled vegetables and torn herbs in a large bowl.
Cut lamb into chops. Divide vegetable mixture evenly among 8 plates; top evenly with chops (about 3 chops each). Top each chop with 1 (1/4-inch-thick) slice of demi-glace butter; drizzle vegetables and chops with balsamic glaze to taste.