In a large bowl, whisk yogurt and tandoori seasoning until blended.
Add chicken and turn to coat. Cover and refrigerate at least 30 minutes or overnight, turning occasionally.
In a small bowl, combine slaw ingredients. Refrigerate, covered, until serving.
For sauce, combine yogurt, mint, lime juice, garlic, salt and pepper. Refrigerate, covered, until serving.
Drain chicken, discarding marinade. In a large cast-iron or other heavy skillet, heat oil over medium heat.
Add chicken; cook until a thermometer reads 170°, 5-6 minutes on each side.
Spread sauce over toasted bun tops. On each bun bottom, layer lettuce, chicken and slaw. Replace tops.
