In a small bowl, whisk together 1 tablespoon soy sauce, rice vinegar, honey, and 1 tablespoon cornstarch with a splash of water until smooth. This will be your quick sauce.
Heat a large skillet or wok over medium-high heat. Add the neutral oil and swirl to coat. Add the ground chicken and cook, breaking it up with a spatula, until it starts to brown and seems opaque in most places, about 4-5 minutes.
Push the chicken to the edges of the pan. In the center, add a touch more oil if the pan looks dry. Add garlic and ginger, cooking for about 30 seconds until fragrant.
Stir in the broccoli and bell pepper. Cook for 2-3 minutes until they just begin to soften but still have minor crunch.
Pour the prepared sauce over the chicken and vegetables. Stir well to coat everything. If the sauce seems too thick, splash in a little rice wine or water to loosen it.
Add the remaining 1 tablespoon soy sauce and the chopped green onions. Cook for another 1-2 minutes, letting the sauce thicken and glaze the ingredients.
Turn off the heat. Sprinkle with sesame seeds. Taste and adjust with a pinch of salt or a few more drops of soy sauce if needed.
Serve hot over cooked rice or noodles. Leftovers can be stored in an airtight container for up to 3 days.