Combine chicken with 2 tablespoons olive oil, coconut sugar, and 1 teaspoon chicken salt in a mixing bowl, tossing well to coat. Let sit at room temperature while preparing the vegetables.
Combine all the peppers with 2 tablespoons olive oil, 1 teaspoon chicken salt, onion, chickpeas, and garlic on a sheet pan or baking dish. Give a toss and spread into an even layer. Top with prepared chicken. Pour the vinegar over the entire dish. Top each piece of chicken with a generous pinch of furikake. Roast for 30 minutes or until the chicken reaches an internal temperature of 165°F. Remove the chicken from the sheet pan and let rest. Turn the broiler to high.
Toss the vegetables gently and broil for 2–3 minutes. Remove from oven and stir in the butter and tamari. Add chicken back to sheet pan, garnish with parsley and more furikake.