Soak the cedar planks in water for at least 1 hour.
In a small, non-reactive bowl combine the vinegar and shallot. Finely grate the zest from one of the oranges, and then peel and segment both oranges, reserving the juice. Set aside the orange segments. Whisk the orange juice (there should be about 60 millilitres) into the vinegar and shallot. Drizzle in the oil, whisking constantly and then season with salt and pepper.
Prepare the grill for direct cooking over medium–high heat (190ºC to 230ºC).
Rinse the trout under cold water and pat dry with paper towels. Lightly brush the inside of the trout with oil and generously season with salt and pepper.
Place the soaked planks over direct medium–high heat and close the lid. After 5 to 10 minutes, when the planks begin to smoke and char, turn them over and then place two trout, slightly overlapping, on each plank. Grill over direct medium–high heat, with the lid closed, until the fish are firm to the touch and cooked through, 6 to 8 minutes.
Using a spatula, carefully lift each fish onto an individual serving plate, skin-side down and open like a book.
Put the arugula in one bowl and the orange segments and fennel in another. Season both with salt and pepper and toss with vinaigrette. Spoon some of the orange–fennel mixture over each fish, top with the dressed greens and garnish with the remaining orange and fennel mixture.