In a food processor, pulse the chile and ginger until very finely chopped. Add the canned tomatoes with their juice and process until the mixture is pureed. Set aside.

Melt 6 tablespoons of the butter in a 6- to 8-quart Dutch oven over medium heat. When the foam subsides, add about a third of the chicken pieces and cook, stirring frequently, until the chicken absorbs some of the butter and begins to brown, 3 to 4 minutes. With a slotted spoon, transfer the chicken to a plate. Repeat with the remaining two batches of chicken.

Add the remaining 2 tablespoons butter to the pan. When it's melted, add the paprika and 4 teaspoons of the cumin and stir until the spices just begin to darken, 10 to 15 seconds.

Immediately add the tomato mixture. Simmer vigorously, uncovered, stirring frequently, until the sauce has thickened slightly, 6 to 8 minutes. Add the cream and 1 teaspoon kosher salt and stir well.

Add the chicken and stir gently to mix. Reduce the heat to medium low and simmer, uncovered, stirring occassionally, for 10 minutes. Stir in the garam masala and remaining cumin. Remove from the heat, cover, and allow to rest for 15 minutes. Taste and add more salt if necessary.

Transfer to a serving bowl, garnish with cilantro, and serve.

Marinate the chicken: Remove the skin and trim excess fat from the chicken. With a sharp chef's knife, cut three or four long, diagonal slits on each thigh against the grain, almost to the bone.

In a large, shallow bowl, mix together the yogurt, lemon juice, ginger, garlic, coriander, cumin, garam masala, kosher salt, and cayenne. Add the chicken, turning to coat and making sure that the marinade gets into all of the slits in the chicken. Cover and marinate in the refrigerator, at least 2 hours and up to 12 hours.

To roast the thighs for Chicken Tikka Masala: Position a rack in the center of the oven and heat the oven to 375 degrees F. Line a large rimmed baking sheet with foil. Transfer the chicken from the marinade to the baking sheet, spacing the thighs evenly. Discard any remaining marinade. Roast until the juices run clear when the chicken is pierced and an instant-read thermometer in a meaty part of a thigh registers 170 degrees F, about 45 minutes.

Squeeze the lemon halves over the chicken. Let it cool before using in the Chicken Tikka Masala recipe. Refrigerate if making ahead.