Season chicken thighs with sea salt and spread ginger slices and green parts of the green onion on top. Arrange each pair of chicken thighs in an even layer in 2 shallow, heatproof bowls.
Fill a large pot with 4 to 5 inches of water and insert two steam racks inside. Set the bowls on the steam rack and pour 1/4 cup water and coconut juice evenly between the 2 bowls. Cover pot and bring water at the bottom of the pot to a boil; reduce heat to a simmer. Cook chicken breasts until no longer pink at the bone and the juices run clear, about 35 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).
Combine fish sauce, rice vinegar, lime juice, Thai chiles, cilantro stems, garlic, chopped ginger, and palm sugar in a food processor; pulse mixture until well combined. Transfer the sauce mixture into a medium bowl; add green parts of the green onion.
Heat vegetable oil on a skillet over medium heat until smoking, about 4 minutes; pour oil into the sauce mix.
Remove the 2 bowls from the pot. Discard ginger and green onion pieces.
Drain remaining coconut juice liquids, through a sieve, into the sauce mixture. Pour over chicken, and garnish with cilantro leaves.