How to Make It
Stir together sugar, salt, and 1/2 cup of the rice vinegar in a medium bowl until dissolved. Stir in carrots; let stand until carrots begin to soften, at least 10 minutes or up to 30 minutes.
Meanwhile, heat 3 teaspoons of the sesame oil in a large saucepan over medium-high. Add ginger and garlic, and cook, stirring often, until aromatic, about 1 minute. Add turkey; cook, stirring occasionally, until turkey is crumbled, lightly browned, and cooked, 6 to 7 minutes. Stir in fish sauce and 1 1/2 tablespoons of the soy sauce until fully coated.
Whisk together peanut butter, water, honey, Sriracha, and remaining 1 1/2 teaspoons soy sauce, 1/2 teaspoon sesame oil, and 1 teaspoon rice vinegar in a small bowl until well combined.
Divide turkey mixture evenly among lettuce leaves; top with pickled carrots and peanut sauce. Sprinkle with cilantro, mint, and peanuts.