Prepare a charcoal or gas grill for indirect medium heat (350° to 450°; you can hold your hand 5 in. above cooking grate only 5 to 7 seconds). If using charcoal, light 60 briquets and let burn until covered with ash, 15 minutes. Bank evenly on 2 sides. The area over the cleared section is the indirect heat area. If using gas, turn all burners to high, close lid, and heat for 10 minutes. Then turn off 1 burner and reduce others to medium. The area over the turned-off burner is the indirect heat area.
In a large bowl, toss together all but the last 3 ingredients. Spread vegetables on a large rimmed baking sheet (not nonstick).
Cook vegetables over indirect heat, lid down, until very tender, about 60 minutes (for charcoal, add 4 briquets to each side every 30 minutes and keep measuring heat), gently stirring every 15 minutes. Drizzle with vinegar, stir, and cook 15 minutes more. Let vegetables cool. Put in a medium bowl, toss with pine nuts and salt to taste, and sprinkle with cheese.
Note: Nutritional analysis is per serving (about 3/4 cup).