How to Make It
In a medium bowl, toss the cucumbers, onion, vinegar, 1 tablespoon of the sugar and 1 teaspoon of salt. Season with pepper and let stand for 1 hour at room temperature.
In a mortar or medium bowl, using the back of a spoon, mash the ginger with the garlic, chile and remaining 1 teaspoon of sugar to a paste. Stir in the fish sauce, cilantro and basil. On a clean cutting board, thinly slice the tuna. Stack the slices and cut into thin matchsticks. Cut the matchsticks into rough cubes, then chop until the pieces are roughly 1/8 inch. Add the tuna to the ginger paste and stir until evenly combined.
Using lightly moistened hands, shape the tuna mixture into 4 patties about 1 inch thick. Set them on a large plate lined with plastic wrap. Refrigerate the tuna burgers for 20 minutes.
Light a grill. In a small bowl, combine the vegetable oil with the sesame oil. Lightly brush the burgers and the cut sides of the buns with oil. When the fire is medium hot, brush the grate with oil. Grill the burgers for 6 minutes, turning once, for medium rare. Move the burgers away from the heat and grill the cut sides of the buns until toasted, 1 minute.
Drain the cucumber salad. Spread the Ginger-Lemon Mayonnaise on the cut sides of the buns and set the tuna burgers on the bottoms. Top with the cucumber salad and peanuts. Cover the burgers with the buns and serve.