Heat 2 tablespoons of coconut milk (the cream-like part) in a large saucepan or pot over medium heat. Add the shallot, garlic and ginger. Cook for 2–3 minutes, stirring frequently, until softened and fragrant.
Stir in the almond butter, yellow curry paste, soy sauce and sugar. Cook for about 1 minute, stirring continuously, until smooth and aromatic.
Pour in the remaining 1 cup coconut milk and 1 cup water. Whisk until the sauce is smooth.
Bring the sauce to a gentle boil, then reduce the heat to low. Simmer uncovered for 5–10 minutes, stirring occasionally. Add more water as needed until the sauce reaches your preferred consistency.
Remove the pot from the heat and stir in the lime juice. Taste and adjust with additional soy sauce, lime juice or sugar as desired.
To serve, divide the rice among bowls and spoon the curry sauce over the top. Slice the chicken thighs and arrange them over the rice. Finish with additional lime juice and serve immediately.