4 garlic cloves, finely grated
1 (3") piece ginger, finely grated
1 (14-ounce) can coconut milk
3 teaspoons finely grated lime zest
2 tablespoons fresh lime juice
2 tablespoons tomato paste
3 teaspoons kosher salt
1 1/2 teaspoons ground turmeric
1/4 teaspoon cayenne pepper
1/4 teaspoon ground cardamom
2 pounds boneless skinless chicken thighs, trimmed, cut into 1 1/2" cubes
1 medium eggplant, cut into 1 1/2" cubes
1 small red onion, cut into 2" pieces
1 pint cherry tomatoes
Canola or vegetable oil (for grill)
Naan or flatbread, cilantro, lime wedges, and plain yogurt (for serving)
14 (8–12-inch-long) metal or bamboo skewers soaked in water at least 1 hour
Whisk garlic, ginger, coconut milk, lime zest and juice, tomato paste, salt, turmeric, cayenne, and cardamom in a large bowl. Transfer half of marinade to another large bowl. Add chicken to 1 bowl of marinade; toss to coat. Add eggplant, onion, and tomatoes to the other bowl; toss to coat. Cover and chill at least 1 hour.
Thread each ingredient onto its own set of skewers: divide chicken among 6 skewers, tomatoes among 4, eggplant among 3, and onion on 1.
Prepare a grill or grill pan for high heat; generously oil grates. Grill skewers, turning often, until well charred and cooked through, about 5 minutes for tomatoes, 10 minutes for chicken, and 15 minutes for eggplant and onion.
Just before serving, toast naan on grill until warmed through, about 2 minutes. Top grilled chicken and vegetables with cilantro and serve with naan, lime wedges, and yogurt alongside.
Ingredients can be marinated 1 day ahead; cover and chill. Skewers can be assembled 1 day ahead; cover and chill.