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1
Remove tough outer layers from lemongrass. Finely grate bottom third of 1 stalk and set aside; discard the rest of the stalk. Trim and discard top third of remaining stalk, then bruise stalk by giving it a few whacks against a cutting board (this helps release the essential oils). Tie it in a loose knot; set aside.
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2
Pulse reserved grated lemongrass with shallot, garlic, ginger, red pepper flakes, turmeric, and 2 Tbsp. water in a food processor, adding a splash or two of water if needed, until a paste forms.
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3
Heat oil in a large skillet over medium. Season chicken with salt and pepper and cook, skin side down, until skin is lightly browned and crisp, 8-10 minutes. Transfer to a plate.
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4
Cook spice paste in same skillet, stirring, until very fragrant, about 5 minutes (it will begin to darken slightly as the water evaporates and the paste begins to fry in the fat left behind).
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5
Add kaffir lime leaves (if using), cinnamon, cardamom, star anise, coconut milk, coconut sugar, and reserved knotted lemongrass to skillet. Bring to a simmer, add chicken, and cook, turning pieces occasionally and scraping bottom of skillet often, until chicken is falling-apart tender and coconut milk has broken (the fat will separate from the liquid and start to brown the chicken and other aromatics), about 1 1/2 hours.
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6
Toast shredded coconut in a dry small skillet over medium heat, tossing occasionally, until golden brown, about 5 minutes. Let cool.
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7
Arrange chicken on a platter and spoon any braising liquid over. Top with cilantro, chives, and toasted coconut.
