Add the water to a large stock pot and bring to a boil. Once boiling, add the crab halves. Reduce the heat to medium, cover, and simmer for 5 minutes to partially cook the crab. Drain the crab and discard the water. Place the crab on a plate and set aside.

Place the pot back on the stove over medium-high heat. Once hot, add the coconut oil and let it melt. Then add the shallots and lemongrass. Cook for 2 to 3 minutes, until the shallots have begun to soften. Add the garlic, ginger, and Thai green chilis and cook for 30 seconds, until fragrant. Add the coconut milk, water, and fish sauce, followed by the crab. Toss the crab in the coconut broth, cover, and simmer over medium heat for 5 minutes to fully cook the crab.

Remove the crab from the pot and arrange on a serving platter. Pour over all the coconut broth and garnish with fresh Thai basil leaves and lime zest. Serve immediately and enjoy!