Heat 1 tablespoon of oil in a large skillet or wok over medium-high heat.
Add the sliced chicken, season lightly with salt and pepper, and stir-fry until cooked through and lightly browned, about 5-7 minutes. Remove chicken and set aside.
In the same skillet, add garlic and ginger, sauté for 30 seconds until fragrant.
Add broccoli florets and stir-fry for 3-4 minutes until bright green and slightly tender.
Return chicken to the skillet, then pour in soy sauce, oyster sauce, hoisin sauce, chicken broth, and red pepper flakes. Stir to combine.
Add the cornstarch slurry, stirring constantly until the sauce thickens, about 1-2 minutes.
Stir in cooked brown rice and green onions, tossing to mix well and heat through.
Adjust seasoning with salt and pepper if needed, then serve hot.