Toss the cubed chicken with the whites of the green onions, sugar, sesame oil, soy sauce, half the garlic, half the ginger, 1 teaspoon of cornstarch, and 3/4 tsp salt. Set aside and let marinate on counter for about 15 minutes. In a separate small bowl, combine the remaining tablespoon of cornstarch with 1/3 cup water and save for later.
Add 1 tablespoon vegetable oil to a large skillet and heat over medium high heat. Add broccoli florets, remaining garlic and ginger, 2 tbsp water, and pinch of salt and black pepper. Stir-fry until broccoli is bright green but still crisp, about 2 minutes. Transfer to a plate.
Add remaining 1 tbsp vegetable oil to same skillet. Add cubed chicken mixture along with red pepper flakes. Stir-fry for about 5-6 minutes, tossing chicken frequently. Add hoisin sauce and broccoli florets to pan and toss to mix together until evenly coated with sauce. Pour in the cornstarch and water mix and this will thicken up the sauce. Add a tbsp or two of water if you need to thin it down. Cook another 3-5 minutes to ensure chicken is cooked thoroughly and test one of the larger cubes of chicken to ensure chicken is cooked through. Serve alongside jasmine rice