1 (1 by 4-inch) untreated cedar plank, soaked overnight in water
Preheat the oven to 375 degrees F.
To make the croutons: Cut the bread into squares. Combine melted butter and olive oil. Toss bread squares in the oil and melted butter combination and season with salt and pepper. Place on a baking sheet in 1 layer. Bake, tossing several times in the cooking process, until they are golden brown, crispy on the outside and a little soft inside, 10 to 15 minutes. Cool at room temperature and reserve. Do not refrigerate.
To make the vinaigrette: In a food processor, add garlic, lemon juice, vinegar, anchovy fillet, Dijon, Worcestershire, hot sauce, salt, pepper, and egg yolk and process for 15 seconds. With the processor running, slowly drizzle in the truffle oil and the olive oil. This recipe will make twice the amount that you need for a salad for 6 people.
It is difficult to make a smaller quantity in a food processor. The vinaigrette will keep up to 1 week, well covered, in the refrigerator. The salad is good enough to serve twice in 1 week.
Preheat a grill to high.
To make the Salad: In a mixing bowl, drizzle the chunks of salmon with enough oil just to coat. Season with salt and pepper. Remove the plank from the water and brush with some oil. Place the plank either on the grill or next to an open fire in a wood oven. Allow it to just catch fire. Put it out, and do the same to the other side of the plank. Place the fish pieces directly onto the plank, about 1-inch apart. Return it to the grill. The plank should be arranged near the fire so that it smolders on the edges, creating smoke that surrounds the fish. Allow this to continue, placing it near the fire in such a way that it smolders but does not catch fire.
Cook the fish to medium rare, about 6 minutes.
While the salmon is cooking, place the whole, but separated romaine leaves in a large mixing bowl with the croutons. Ladle about 1/2 of the vinaigrette over the whole leaves, season with salt and pepper and toss just to coat the leaves. Sprinkle the grated Parmesan over the salad and give the salad a final gentle toss. Arrange the leaves and the croutons on 6 chilled plates. Flake the salmon on its natural separations and divide evenly over the salads.