1. In a food processor, puree ginger, onion, and garlic to a paste. Add 1/4 cup of mixture to yogurt in a large bowl, reserving remainder. Season chicken with salt, pepper, and 1 teaspoon tandoori spice. Add to yogurt mixture; toss to combine. Let stand 30 minutes; meanwhile, preheat broiler.

2. Transfer chicken to a broiler pan and broil until browning in spots, 5 to 6 minutes. Flip and brown on second side, 5 to 6 minutes more. Remove from broiler. (It won't be cooked through.)

3. Heat a large straight-sided skillet over medium-high. Swirl in oil. Add reserved onion paste; cook until fragrant, about 2 minutes. Add remaining 2 teaspoons tandoori spice; cook 30 seconds. Stir in tomatoes, 1/2 cup water, and chicken. Bring to a boil, then reduce heat and simmer, covered, until chicken is tender, about 25 minutes. Use 2 forks to shred chicken into bite-size pieces. Season with salt and pepper; serve with naan, cucumbers, herbs, and more yogurt.