1. Preheat oven to 400 degrees. Let duck breasts stand for 30 minutes at room temperature.

2. Heat duck fat in a large heavy-bottomed ovenproof skillet over medium heat. Add mustard seeds and curry leaves. Let cook, stirring constantly, until mustard seeds begin to pop, about two minutes. Add pepper and coconut milk; bring to a boil. Reduce heat to a simmer and add curry powder and tamarind paste; let simmer for 15 minutes. Season with 1/2 teaspoon salt; remove from heat and set sauce aside.

3. Lightly score skin of each duck breast on the diagonal 1-inch apart, taking care not to cut flesh. Season with salt and let stand for 10 minutes. Heat a large heavy-bottomed skillet over medium heat; add duck breasts, skin-side down. When they begin to sizzle, reduce heat to medium-low; cook until fat is rendered and skin is browned.

4. Transfer duck breasts to skillet with sauce, skin side up, reserving rendered fat for another use. Transfer skillet with sauce and duck to oven and cook 10 minutes for medium and 15 minutes for well done.

5. Remove breasts from sauce and let stand 5 minutes. If coconut milk in sauce has begun to separate, stir in heavy cream. Slice each duck breast on the diagonal against the grain. Serve immediately with sauce, rice, and naan.