Season the chicken all over with the salt and allow to marinate for 30 minutes, or cover and refrigerate overnight.
Spread the green onions and ginger in the donabe. Add the chicken and spread out in a single layer. Add the shochu, soy sauce, brown sugar, and vinegar over the chicken.
Spread out the cabbage to cover the chicken entirely. Cover with the lid and set over medium-high heat. Cook for 5 minutes. Turn down the heat to medium-low and cook for 25 to 30 minutes longer, or until the sauce has reduced by half or more, stirring occasionally. Turn off the heat and let it rest for 5 to 10 minutes.
Serve in individual bowls at the table and sprinkle with chives and ichimi togarashi.