In a small bowl, whisk together soy sauce, rice vinegar, honey, cornstarch, grated garlic, and grated ginger until cornstarch is suspended.
Heat 1 tablespoon olive oil in a large frying pan or wok over medium-high heat until shimmering.
Add ground chicken, half the kosher salt, and black pepper. Cook, breaking up meat, until browned and cooked through, about 5 to 7 minutes.
Transfer chicken to a plate and set aside.
Heat another tablespoon of olive oil in the same pan over medium-high heat until shimmering.
Add diced onion and red bell pepper. Cook, stirring occasionally, until onion softens, about 3 to 4 minutes.
Transfer vegetables to the plate with chicken.
Heat the remaining tablespoon of olive oil in the pan over medium-high heat until shimmering.
Add chopped cabbage and season with remaining kosher salt. Cook, tossing occasionally, until crisp-tender and lightly browned, about 2 to 3 minutes.
Reduce heat to medium and return chicken, onion, bell pepper, and any juices to the pan.
Rewhisk the sauce, then pour it into the pan. Cook, tossing regularly, until sauce thickens and coats ingredients, about 1 minute.
Garnish with sliced scallions if desired. Serve with steamed rice or noodles as preferred.