Make the marinade for the chicken: Place chicken thighs in a resealable plastic bag. In a small bowl, whisk garlic, ginger, yogurt, lime juice and spices until smooth. Pour over chicken thighs. Seal bag and allow chicken to marinate in refrigerator at least 4 hours or overnight.

While chicken marinates, prepare the sauce: Place quartered tomatoes in food processor and pulse several times until tomatoes are a slightly-chunky sauce. Set aside.

In a large saucepan over medium-high heat, heat oil until shimmery. Add onion, garlic, and ginger to pan. Stir occasionally until mixture is slightly-softened, about 5 minutes. Stir paprika, garam masala, tumeric, and tomato mixture into onions. Bring mixture to a simmer, stirring frequently.

Remove sauce from heat and transfer to a blender. Blend on high speed until completely smooth. Return sauce to pan and season with salt and pepper to taste. Bring sauce to a low simmer, then reduce heat to low and cover. Stir occasionally until sauce is reduced and slightly-thickened, about 20 minutes.

Cook the chicken: Remove chicken from marinade and discard marinade. Grill chicken over medium-high heat, turning occasionally until juices from chicken run clear. Let chicken cool slightly, then dice each thigh into 1-in cubes. Add chicken to sauce and sprinkle cilantro over top. Serve chicken tikki masala warm with rice.