Place the salmon in baking dish with the soy sauce, liquid smoke, and brown sugar. Let it marinate for at least 1 hour—but you could marinate overnight. Flip once. When ready to use, preheat the grill or an iron skillet to high heat.
Peel the ginger and cut into thin (julienne) strips. Heat a small skillet over medium-high. Add 1 tablespoon of oil to the skillet. When the oil is hot, drop the ginger in and pan-fry for 1-2 minutes, moving with a spatula, until they are light brown. Remove from the pan and drain on a paper towel. Sprinkle with salt.
Carefully brush the grill with vegetable oil. (You could also use grill spray.) Pepper the salmon and place it on the grill, top-side-down. Cook 3 minutes. Flip, then carefully sprinkle the tops with a little extra brown sugar and grill for another 3-5 minutes—until just cooked through. Serve warm with fried ginger on top.