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.