Pour 1/2 of the coconut milk in a pan over medium heat. Add curry paste and break it up to mix it with coconut milk. Keep stirring to prevent bottom from sticking.
Lower the heat to simmer if necessary. Simmer until red oil appears.
Add the beef and stir to coat the beef with the curry paste.
Add sugar, fish sauce and the rest of coconut milk. Let it simmer until the beef is tender and the liquid is reduced to a thick sauce. It should take about half an hour to an hour depending on your heat.
Add water if your beef is still tough and let the liquid reduce.
Sprinkle the sliced kaffir lime leaves on top. Serve hot.