Make ginger sauce by combining the first 6 ingredients in a small bowl. Cover and refrigerate until needed.
Preheat your barbecue or indoor grill to medium-high. Brush salmon with the 2 Tbsp. oil. Lightly oil the bars of the grill. Grill salmon 3 to 4 minutes per side, or until just cooked through.
Spread the baguette or buns with the ginger sauce. Divide and set lettuce on each piece of baguette or bun. Set on the salmon. Divide and top salmon with carrot and cucumber. Drizzle the fish with hot sauce, if using, and serve.
Recipe Options: For another taste element, mix 2 Tbsp. of chopped fresh cilantro or mint into the ginger spread on the bread. Instead of shredded leaf or head lettuce, use baby mix salad greens in these sandwiches. For a more pungent topping, instead of grated carrot, top the fish with some very thin slices of radish.