Preheat broiler with a rack set about 3 in. from heat. Toast pine nuts in a medium frying pan over medium-low heat until golden, stirring often, 4 to 7 minutes. Pour into a bowl and let cool.
Set salmon and grapes on a rimmed baking sheet, leaving some space around fish. Drizzle everything with 1 tbsp. oil and sprinkle with 1 tsp. thyme and 1/4 tsp. each salt and pepper. Turn fish and grapes to coat, setting salmon skin side down if fillets have skin.
Broil until fish is still a bit rare in center (cut to test), 4 to 6 minutes; fillets will continue to cook as they sit. Grapes should be a bit wrinkled; if not, transfer fish to a plate and broil grapes a few minutes longer. Sprinkle fish and grapes with remaining 1/2 tsp. thyme.
In a small bowl, whisk together remaining 5 tbsp. oil, 1/2 tsp. salt, and 1/4 tsp. pepper with the vinegar, mustard, and garlic until emulsified. In a large bowl, toss arugula with half of pine nuts and a third of balsamic dressing.
Arrange salad on a platter. Set salmon on top, overlapping pieces a bit. Gently combine remaining pine nuts with grapes; spoon grape mixture over fish. Serve with remaining dressing on the side and lemon wedges if you like.
*Ask your fishmonger to remove bones, or go to sunset.com/salmonvideo to see how.