Toast coconut: Heat a skillet over medium-low heat. Add the shredded coconut and toast, stirring occasionally, until golden brown. Transfer to a bowl and set aside.
Make curry paste: If using dried chilies, simmer them in boiling water for 5-10 minutes, until softened. Add 1/2 cup of the simmering liquid (or water if using fresh chilies) to a high-powered blender. Chop the tops off the chilies (keep the seeds) and add to the blender along with all remaining curry paste ingredients; blend until very smooth. Add up to ¼ cup additional liquid if needed to blend; set aside.
Sear beef: Heat 1 tablespoon oil in a 3.5 quart or larger Dutch oven over high heat. Once hot, add half the beef and sear on all sides; remove to a plate and repeat with remaining beef.
Make curry: Reduce heat to medium-low. Add curry paste to the empty pot and cook for 4-5 minutes or until the moisture reduces and the curry thickens into a paste and begins to caramelize.
Braise: Add all of the braising ingredients to the pot with the curry paste, including the beef. Bring to simmer, then reduce heat to the lowest setting to maintain a very gentle simmer. Cover and simmer for 1 1/2-2 hours, stirring occasionally, until very tender. Stir often (and recover) the last 30 minutes so it doesn’t burn.
Reduce: This step may not be needed if your sauce reduced completely with the lid covered. Remove the lid and continue to cook until the beef is fall apart tender and sauce thickens into a paste to coat the beef, about 20 minutes, stirring often. If the sauce thickens too much before the beef is done, add a water and continue to cook until fall part tender.
Serve: Discard lemongrass, star anise and cinnamon before serving. Serve with coconut rice and limes.