1 1/2 bone-in, skin-on chicken breasts
2 3/4 cups canola oil
1 coconut, cracked open and shredded
12 small Asian shallots or 4 medium regular shallots, thinly sliced
1/4 tsp. freshly grated nutmeg
1/4 tsp. whole black peppercorns
1/4 tsp. whole corainder
1 Balinese long pepper (optional)
2 tsp. ground tumeric
16 cloves garlic, peeled
3 candlenuts or unsalted macadamia nuts
1 (1/2″) piece galangal, peeled and thinly sliced
2/3 cup coconut milk, preferably UHT from a carton
1/2 tsp. Indonesian shrimp paste
5 small red Thai chiles, stemmed
1 Holland chile, stemmed
Kosher salt, to taste
4 fresh or frozen Kaffir lime leaves, thinly sliced
Juice of 1 lime
Cooked white rice, for serving
Heat a charcoal grill or set a gas grill to medium-high. (Alternatively, heat a cast-iron grill pan over medium-high.) Rub chicken with 2 tbsp. oil; grill, flipping once, until cooked through, 40–45 minutes. Let cool, then discard bones; finely shred meat and skin. Transfer to a bowl.
Heat a 12″ nonstick skillet over medium-high heat. Cook coconut until golden, 12–15 minutes; add to chicken. Add 2 cups oil and 3?4 of the shallots to pan; heat over medium. Cook, stirring occasionally, until shallots are golden brown and crisp, 10–12 minutes. Using a slotted spoon, transfer shallots to paper towels to drain; set aside. Discard oil.
Grind nutmeg, peppercorns, coriander, and long pepper, if using, in a spice grinder into a powder; transfer to a small food processor.
Add turmeric, half the garlic, the candlenuts, galangal, and 3 tbsp. water; purée into a smooth paste.
Add 2 tbsp. oil to pan; heat over medium-high. Cook paste until fragrant, 2–3 minutes. Transfer to bowl with chicken. Add coconut milk to pan; simmer over medium heat until reduced by half, 2 minutes. Let cool; add to chicken mixture.
Add remaining shallots and garlic, the paste, chiles, and salt to food processor; purée into a smooth paste. Heat remaining oil in a 10? skillet over medium-high heat; fry paste until golden, 6–7 minutes. Let cool; add to chicken mixture.
Stir in half the fried shallots, the lime leaves, and juice; garnish with remaining shallots. Serve with rice.