In a small bowl combine all the butter ingredients and mash together with a fork to mix well. Place the butter on a piece of plastic wrap. Roll up the plastic to form the butter into a cylinder, (1 to 1¼ inch) thick in diameter. Refrigerate for at least 1 hour to firm up. Cut into (1/2 inch) disks and bring to room temperature before serving.
. In a rectangular baking dish filled with water, submerge the cedar plank. Weigh the plank down with cans and let soak for at least 1 hour.
In a small bowl combine all the oil ingredients.
Place the salmon, skin side down, on a work surface. Score the salmon without piercing the skin into 4 serving pieces. Brush the salmon flesh with about three-quarters of the oil.
. Prepare the grill for direct cooking over medium-high heat (400° to 500°F).
Brush the cooking grates clean. Drain the cedar plank. Place it over direct heat and close the lid. When the plank begins to smoke and toast, after 3 to 10 minutes, use long-handled tongs to turn it over. Slide the salmon, skin-side down, onto the toasted side of the plank. Arrange the lemon slices over the salmon and lightly brush the slices with the remaining oil.
Grill over direct medium-high heat, with the lid closed, until an instant read thermometer inserted in the thickest part of the salmon registers 125° to 130°F (or your preferred doneness), 15 to 30 minutes for medium-rare, depending on the thickness.
To serve, transfer the fillet on the plank to a heatproof surface. Lift the portions from the skin and serve with the lemons and a few pads of lemon butter.