To prepare the glaze: Combine the pineapple juice, vinegar, ginger, soy sauce and brown sugar in a small saucepan and bring to a boil. Reduce the heat to low and simmer until the volume is reduced by half, about 30 minutes. Add the mustard and cook an additional 2 minutes. Remove from the heat and add the lime juice, and white pepper. Let cool.
To prepare the burgers: Shape the ground tuna firmly into 8 round uniform patties about 1 1/2-inches thick. Place in the refrigerator for 30 minutes. (The burgers must be very cold to hold their shape when cooking) Brush both sides of the burgers lightly with the pineapple glaze and season with salt and pepper to taste. Preheat grill. Grill burgers for 3 to 4 minutes on each side for medium doneness, basting often with the glaze. Serve burgers on rolls with watercress.
To prepare the relish: Combine all ingredients in a medium bowl and season with salt and pepper to taste. Let sit at room temperature for 30 minutes before serving.
To prepare the gaufrettes: Heat oil to 365 degrees F in a deep fryer. Fry potato in batches and remove to large plate lined with paper towels. Season immediately with salt and ancho chile powder.