Season the chicken on one side with the salt and some pepper.
In a large dutch oven over medium-high heat, warm 1 tablespoon olive oil. Add the chicken (salted-side-down) and cook for 3 minutes or until browned. Transfer to a plate (you’ll finish cooking it later).
To the pot, add the remaining 1 tablespoon olive oil, onion, carrots, and a pinch of salt. Cook for about 3 minutes or until the onions/carrots have softened, stirring occasionally and scraping up any chicken bits stuck to the pot. Stir in the ginger and cook for 1 more minute, stirring occasionally.
Stir in the rice to combine, then stir in the water, soy sauce, and vinegar. Arrange the chicken (raw side facing down) on top. Pour any juices left on the plate back into the pot.
Bring to a boil, then cover with a tight fitting lid and simmer over low heat for 20 minutes. If the rice is not cooked through at this point, cover and continue to cook (add a bit more water if there isn’t any in the bottom of the pot). Transfer the chicken to your cutting board.
If adding kale, scatter it on top. Cover with the lid and let it simmer for 1-2 more minutes to soften the greens, then fluff/stir to gently mix everything together.
Let the rice sit for 5 minutes while you chop up chicken. You can fish out the big chunks of ginger, though someone will inevitably get a chunk in their bowl!
Serve the rice topped with the chicken and herbs.