Heat 1 tablespoon of the oil in a large skillet or wok over high heat until very hot. Add the chicken in a single layer, cook undisturbed for 2 minutes, then stir-fry until cooked through, 4 to 5 minutes total. Season with salt and pepper, then transfer to a plate.

Reduce heat to medium-high, add the remaining 1 tablespoon oil, then the zucchini in a single layer. Cook undisturbed 2 minutes, stir, and cook 2 more minutes until crisp-tender. Add the garlic and ginger, stirring constantly for 30 seconds until fragrant.

Stir together the soy sauce, honey, rice vinegar, cornstarch, and water until smooth. Pour into the pan, bring to a simmer, and cook until thickened, about 1 minute.

Return the chicken and any juices to the pan. Toss to coat in the sauce and cook 1 minute to heat through. Garnish with green onions and sesame seeds, and serve immediately over rice.