Fill a large bowl with ice water. In a large saucepan, bring 2 quarts water to a boil. Stir in 2 tablespoons salt and the snap peas. Cook until bright green and crisp-tender, about 2 minutes. Drain, then immediately transfer to the ice water. Let stand until completely cooled, about 2 minutes, then drain again. Slice half the peas in half on the bias, then set aside.

In a small bowl, toss half (about ¾ cup) of the tuna with 2 tablespoons of oil, 1 tablespoon of lemon zest, 1 tablespoon of lemon juice, and ¼ teaspoon each salt and white pepper. Set aside.

In a blender, combine the remaining tuna, the remaining 1 tablespoon lemon zest, 1 tablespoon of the remaining lemon juice, ¼ teaspoon white pepper, the fish sauce and mayonnaise. Blend until a smooth paste forms, about 45 seconds, scraping the blender jar as needed. With the machine running, drizzle in 3 tablespoons of the remaining oil and blend until creamy and thick, about another 45 seconds. If needed, drizzle in up to 1 tablespoon water to achieve the proper consistency. Taste and season with salt and pepper, then set aside.

In a large bowl, toss together the peas, radishes, basil and poppy seeds. Add the remaining 2 tablespoons lemon juice, the remaining 2 tablespoons olive oil, and ¼ teaspoon each salt and white pepper. Toss well. On a serving platter, spread about ⅔ cup of the tuna sauce in an even layer. Top with the vegetables, then sprinkle with the flaked tuna. Serve with the remaining sauce on the side.