Fill a large pot with 6 cups of water and add the chicken drumsticks, ginger slices, and the white parts of the scallions. Bring to a boil, then reduce heat and simmer for 10 minutes.

Turn off the heat and cover the pot, allowing the chicken to sit in the liquid for 1 minute. Transfer the chicken to an ice water bath to cool for 20 minutes.

In a mixing bowl, combine olive oil, low sodium soy sauce, coconut sugar, reserved cooking water, chopped ginger, and finely chopped scallions. Stir well until blended.

Shred the tender chicken using two forks and arrange it on a serving plate. Pour the sauce over the chicken, ensuring every piece is coated.