Coat the chicken: Toss the thinly sliced chicken with 1 tablespoon of the cornstarch and 1 tablespoon of the soy sauce until every piece is lightly coated. Let it sit for 10 minutes while you prep everything else.
Whisk the garlic ginger sauce: In a small bowl, whisk the remaining 1 tablespoon cornstarch with the remaining 3 tablespoons soy sauce until smooth and lump-free. Whisk in the chicken broth, rice vinegar, honey, toasted sesame oil, and red pepper flakes if using. Set it near the stove.
Steam the broccoli in the skillet: Heat 1 tablespoon of the vegetable oil in a large skillet or wok over medium-high heat. Add the broccoli and stir for 2 minutes, then pour in the water, cover, and steam for 3 minutes until the florets are bright green and crisp-tender. Transfer them to a plate and wipe the skillet dry.
Sear the chicken: Add the remaining 2 tablespoons vegetable oil to the skillet over high heat. Spread the chicken in a single layer and leave it undisturbed for 1 minute, then toss and cook 3-4 minutes more, until browned and a thermometer reads 165°F. Cook in two batches if the pan is crowded.
Bloom the garlic and ginger: Reduce the heat to medium, push the chicken to one side, and add the minced garlic and grated ginger. Stir for 30-45 seconds, just until fragrant, then toss with the chicken.
Add the sauce: Whisk the sauce again to redistribute the cornstarch, pour it into the skillet, and stir constantly for 1-2 minutes until it thickens and turns glossy enough to coat the back of a spoon.
Return the broccoli and serve: Add the steamed broccoli back to the pan and toss for about 1 minute until everything is coated and hot. Spoon the chicken and broccoli stir fry over cooked white rice and top with sliced green onions and toasted sesame seeds.
Notes
The cornstarch coating on the chicken is a simplified velveting step: it holds moisture in during the sear and gives the sauce something to cling to. Cook the chicken to an internal temperature of 165°F.