1. Make the burgers: Fit a food grinder with a grinding plate with about 1/4-inch holes. Grind tuna into a bowl. Add garlic, ginger, lemon zest, mustard, salt, and pepper. Mix gently, and shape into four 1-inch-thick patties. Cover, and refrigerate until cold and firm, about 30 minutes.

2. Make the coleslaw: Whisk vinegar, sugar, and salt in a small bowl. Mix carrot, radish, cabbage, scallion, and sesame seeds in a medium bowl. Toss slaw with vinegar mixture, and refrigerate up to 1 hour.

3. Heat oil in a large nonstick skillet over medium heat. Cook patties to medium-rare, about 2 minutes per side. Wipe skillet clean, and return to heat. Spread mayonnaise on cut sides of roll halves, and heat, mayonnaise side down, until golden, about 1 minute. Divide burgers and slaw among bottom halves of buns. Sandwich with top halves.