In a small bowl, whisk together soy sauce, oyster sauce, sesame oil, cornstarch, and water. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add ground turkey to the skillet and cook, breaking it apart with a spatula, until browned and cooked through, about 6 to 8 minutes.
Remove the cooked turkey from the skillet and set aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet.
Add minced garlic and ginger to the skillet and sauté for 30 seconds until fragrant.
Add broccoli florets to the skillet and stir-fry for 4 to 5 minutes until they are bright green and tender-crisp.
Return the cooked ground turkey to the skillet with the broccoli.
Pour the sauce mixture over the turkey and broccoli, stirring well to coat everything evenly.
Cook for an additional 2 to 3 minutes, allowing the sauce to thicken and coat the ingredients.
Season with black pepper and red pepper flakes, stirring to combine.
Remove from heat and serve immediately.