For the sauce
4 tablespoons unsalted butter, cut into 4 pieces and chilled, divided
1 onion, chopped fine
5 garlic cloves, minced
4 teaspoons grated fresh ginger
1 serrano chile, stemmed, seeded, and minced
1 tablespoon garam masala
1 teaspoon ground coriander
1/2 teaspoon ground cumin
1/2 teaspoon pepper
1 1/2 cups water
1/2 cup tomato paste
1 tablespoon sugar
2 teaspoons table salt, divided
1 cup heavy cream
For the Chicken
2 pounds boneless, skinless chicken thighs, trimmed
1/2 teaspoon cumin
1/2 teaspoon curry powder
1/2 teaspoon coriander
1/2 teaspoon turmeric
1/2 cup plain Greek yogurt
3 tablespoons chopped fresh cilantro, divided
Sauce
Melt 2 tablespoons butter in large saucepan over medium heat. Add onion, garlic, ginger, and serrano and cook, stirring frequently, until mixture is softened and onion begins to brown, 8 to 10 minutes.
Add garam masala, coriander, cumin, and pepper and cook, stirring frequently, until fragrant, about 3 minutes.
Add water and tomato paste and whisk until no lumps of tomato paste remain.
Add sugar and 1 teaspoon salt and bring to boil.
Off heat, stir in cream.
Using immersion blender, blender or food processor, process until smooth, 30 to 60 seconds.
Return sauce to simmer over medium heat and whisk in remaining 2 tablespoons butter. Remove saucepan from heat and cover to keep warm.
Chicken
Combine chicken, yogurt, remaining 1 teaspoon salt, curry, cumin, coriander, and turmeric in bowl or zip top bag and toss well to coat. Using tongs, transfer chicken to wire rack set in aluminum foil—lined rimmed baking sheet. Broil until chicken is evenly charred on both sides and registers 175 degrees, 16 to 20 minutes, flipping chicken halfway through broiling alternately the chicken can be cooked on a grill or baked in the oven.
Once chicken is cooked, cut into chunks and stir into sauce, heat sauce again on stove.
Serve with basmati rice.