Fill a large pot with 4 to 5 inches of water. Insert a large steam rack inside the pot.

Season chicken thighs with salt and spread ginger slices over top. Arrange thighs in an even layer in a large, shallow, heat-proof bowl. Sprinkle white parts of green onions over top; pour in coconut juice and water. Place the bowl onto the steam rack in the pot.

Cover the pot and bring water to a boil. Reduce the heat to a simmer and cook until chicken is 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°F (74°C).

While the chicken is cooking, combine Thai chiles, cilantro stems, garlic, ginger, fish sauce, vinegar, lime juice, and palm sugar in a food processor; pulse until the mixture is well combined. Transfer sauce to a medium bowl and stir in green parts of green onions.

Heat vegetable oil in a skillet over medium heat until smoking, about 4 minutes. Remove from the heat, pour hot oil into the sauce mixture, and stir to combine.

Use an oven mitt or dish retriever tool to carefully remove chicken bowls from the pot. Transfer chicken to a plate; discard ginger and green onion pieces.

Pour remaining cooking liquid through a sieve into the sauce mixture; stir to combine.