Soak the cedar plank in water for at least 1 hour.
Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Season the salmon portions evenly with 1¼ teaspoons salt and ¾ teaspoon pepper. Remove the soaked plank from the water and place it on the cooking grate over direct heat. Close the lid. After 5 to 10 minutes, when the plank begins to smoke and char, turn it over. Place the salmon portions, skin side down, on top of the plank, and slide the plank over indirect medium heat. Cook, with the lid closed, until the salmon is just opaque in the center and the edges begin to brown slightly, 15 to 20 minutes. Meanwhile, make the salad.
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In a large serving bowl whisk the oil, shallot, vinegar, mustard, ½ teaspoon salt, and ¼ teaspoon pepper to create a dressing. Add the tomatoes, basil, and tarragon. Mix well. Scatter the cheese on top.
Transfer the plank with the salmon to a heatproof surface. Serve warm with the salad.