Mix the last 5 ingredients in a bowl or pan. Place salmon in marinade for 20 minutes—cover both sides and turn occasionally.
Prepare grill–moderate heat. For easier clean up put a little cooking oil on a paper towel and oil the grate. This can also be prepared in an oven—350-375 degrees –with a raised grill insert in an oven-safe pan. Put some foil or parchment paper in the bottom of the pan for easier cleanup. Both can be reused several times.
Grill the fish skin-side up for 6 minutes the turn fish and grill skin-side down. Pour marinade over the fish for extra flavor. Grill another 6 minutes or so, depending on thickness of fish.
Top with freshly chopped parsley. Serve with any sides you like. Particularly good with mixed grilled vegetables and any kind of rice.
Note: An excellent variation is to add freshly grated or even ground ginger to the marinade.