Wash the broccoli well and cut it into small florets. Slice the mushrooms evenly so they cook at the same rate. Mince the garlic and ginger finely for the best flavor throughout the dish.
Heat 1 teaspoon of oil in a large skillet over medium heat. Add the broccoli and mushrooms, then cook until slightly tender but still bright in color. Stir often so the vegetables cook evenly without burning.
Mix the minced garlic and ginger into the vegetables. Cook for about 30 seconds until fragrant and aromatic. Remove the vegetables from the pan and keep them aside on a plate.
Wipe the skillet clean and heat the remaining oil over high heat. Season the chicken pieces with salt and pepper, then spread them in a single layer in the pan. Cook until golden brown and fully cooked through.
Add the cooked broccoli and mushrooms back into the skillet with the chicken. Stir everything together so the flavors begin to combine. Let it cook for another 2 minutes over medium heat.
In a small bowl, whisk together oyster sauce, chicken broth, sugar, sesame oil, and soy sauce. In another bowl, mix cornstarch with a tablespoon of cold water. This slurry helps thicken the sauce beautifully.
Pour the sauce into the skillet and stir well. Add the cornstarch slurry and let the mixture simmer until the sauce thickens slightly. The glossy sauce should coat the chicken and broccoli perfectly.
Turn off the heat and serve the stir fry immediately. I love serving it over steamed rice or noodles for a complete meal. Garnish with green onions or sesame seeds for extra flavor and presentation.