In a medium saucepan over low–medium heat, add 2 teaspoons vegetable oil, then sauté the minced garlic and minced ginger for about 30 seconds until fragrant.
Whisk in the brown sugar, red pepper flakes, soy sauce, rice vinegar, and water; simmer and stir until the sauce slightly thickens, about 5–10 minutes. Remove from heat and set aside.
Place the sliced chicken in a large bowl and toss with the cornstarch until pieces are evenly coated.
Heat 1 cup vegetable oil in a large skillet or deep pan over medium–high heat until hot. Fry the coated chicken in batches until browned and cooked through, about 1–2 minutes per batch. Stir so pieces cook evenly.
Transfer cooked chicken to a paper towel–lined plate to drain and discard the frying oil when finished.
Return the skillet to medium heat, add the chicken back in, pour the prepared sauce over the chicken, and cook, stirring, 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.