Soak 24 short bamboo skewers in water for 30 minutes. Thinly slice the chicken breast lengthwise into 24 strips and thread them, through their long sides, onto the skewers. Arrange on a baking sheet.
In a small bowl, combine the curry powder, cumin, 1/2 teaspoon salt and 1 teaspoon pepper. Brush the chicken strips on both sides with the 2 tablespoons peanut oil and sprinkle all over with the dry ingredients. Refrigerate for 1 hour.
In a food processor, combine the rice vinegar, mayonnaise, soy sauce, mint, coriander and 1/4 teaspoon each salt and pepper. With the machine on, slowly drizzle in the 1/2 cup peanut oil and process until smooth. Transfer the vinaigrette to a dipping bowl, cover and refrigerate until ready to serve.
Preheat a stovetop grill pan over high heat. Working in batches if necessary, grill the chicken skewers, turning once, until cooked through and nicely browned, about 2 minutes per side. Serve with the vinaigrette.