In a small bowl, mix the cornstarch and water until smooth and set aside.
Heat 1 tablespoon of olive oil in a large skillet or wok over medium-high heat.
Add the chicken pieces to the skillet and cook for 5-6 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of olive oil.
Add the minced garlic and grated ginger to the skillet and sauté for 30 seconds until fragrant.
Add the broccoli florets and chicken broth to the skillet. Cover and steam for 3-4 minutes until the broccoli is tender-crisp.
Return the cooked chicken to the skillet.
Add the soy sauce, oyster sauce, and black pepper. Stir to combine.
Pour the cornstarch mixture into the skillet and stir well. Cook for an additional 1-2 minutes until the sauce thickens and coats the chicken and broccoli evenly.
Remove from heat and serve immediately.