In a large mixing bowl, combine the yogurt, lemon juice, vegetable oil, garlic paste, ginger paste, tandoori masala, ground cumin, ground coriander, paprika, salt, black pepper, and cayenne pepper. Whisk until smooth and well combined. This marinade will tenderize the chicken and infuse it with flavor.

Add the chicken thighs to the marinade, ensuring they are fully coated. Cover the bowl with plastic wrap and refrigerate for at least 2 hours, or overnight for best results. The longer the chicken marinates, the more flavorful it will be.

Preheat your grill to medium-high heat (about 400°F or 200°C). If using an oven, preheat to 425°F (220°C). This step is crucial for achieving a nice char on the chicken.

Remove the chicken from the marinade, allowing excess marinade to drip off. Place the chicken on the grill. Cook for 6-8 minutes on each side, or until the internal temperature reaches 165°F (75°C). Use a meat thermometer to ensure accuracy.

If using an oven, place the chicken on a baking tray and bake for 25-30 minutes, turning halfway through.

Once cooked, remove the chicken from the grill and let it rest for 5 minutes. Garnish with chopped cilantro and serve with lemon wedges on the side for a fresh burst of flavor.