Make the sauce: heat 2 tablespoons vegetable oil in a medium saucepan over low–medium heat, add the minced garlic and ginger and cook, stirring, for about 30 seconds.
Whisk in the brown sugar, red pepper flakes, soy sauce, rice vinegar, and water, then simmer until slightly thickened, about 5–10 minutes; remove from heat and set aside.
Toss the sliced chicken with the cornstarch in a large bowl until evenly coated.
Heat 1 cup vegetable oil in a large skillet or wok over medium–high heat until hot. Fry the chicken in batches, 1–2 minutes per side, until browned and cooked through; transfer to a paper towel–lined plate and drain excess oil.
Discard the frying oil from the skillet, return the skillet to medium heat, add the fried chicken and pour in the prepared sauce.
Cook and toss the chicken in the sauce over medium heat until the sauce thickens and coats the chicken, about 2–3 minutes.
Stir in the sliced green onions, sprinkle with sesame seeds, and serve immediately over rice.
