Fire up the grill, with the coals lined up under the fish for direct grilling.
Sprinkle sea salt generously in the cavity of the fish and over the skin, then stuff it with the onions, lemons, fronds, and herb sprigs. Tie butcher string around the fish in three or four places to hold the stuffing in. In between the string, make deep incisions with your knife through the thickest part of the fish on both sides, all the way down to the spine. (The fish will cook more quickly, and the smoke flavor will get inside the fish better.) Brush both the fish and the grill lightly with oil, dust the salmon skin on both sides lightly with flour, and place the salmon on the grill.
Grill over medium-hot direct heat, with the cover on and the vents open. When the skin is browned on 1 side, use 2 large metal spatulas to loosen the salmon from the grate and carefully turn over. Continue cooking until just cooked through and an instant read thermometer inserted in the thickest part of the fish registers 135 degrees F to 140 degrees F, about 35 to 40 minutes total cooking time. Remove the fish from the grill and place it on a large platter. Allow the fish to cool for 5 minutes, then remove the butcher string and serve.
*Barbecuing a whole salmon on the grill is a classic Seattle tradition, especially for holidays or special occasions. Tom believes everyone should try cooking a whole fish once in a while- it's not really difficult and it's infinitely more satisfying than always serving boned fillets. Tom strongly recommends using a wild salmon for this recipe, rather than a farmed salmon, because a fish with a nice firm texture is best.