Make a pan out of aluminum foil by doubling up layers of foil large enough to hold your fillet. Place the foil onto a cookie sheet. Lay the fillet onto the foil with the skin side down. In a small bowl, stir together the oil, soy sauce, Worcestershire sauce, lemon juice, ginger, honey, basil and shallots. Pour over the salmon and let it marinate while you preheat the grill, about 20 minutes.
Preheat a grill for medium-low heat. Slide the foil with the salmon off of the cookie sheet and onto the grill. Cover with the lid and grill the fillet for 10 minutes per inch of thickness, about 20 minutes. Salmon should be able to flake with a fork, but not be too dry. When you serve the salmon, the skin will stick to the foil and your grill will remain clean. Simply slice and use a spatula to scoop the fillet off of the skin to serve.