Prepare the broccoli: Steam the broccoli florets with 1 tablespoon of water in a microwave or steamer until they are tender but still bright green (about 3-4 minutes). Set aside.
Cook the shrimp: Heat 1 tablespoon of peanut oil in a large skillet or wok over medium heat. Add the shrimp and cook for 2-3 minutes on each side, until they turn pink and are fully cooked through. Take the shrimp out of the skillet and place them aside.
Make the sauce: In the same pan, add the remaining 1 tablespoon of oil, minced garlic, and ginger. Sa Cook for 1 to 2 minutes until aromatic, making sure the garlic doesn’t burn. Stir in the chicken broth, soy sauce, and oyster sauce, and bring to a simmer.
Thicken the sauce: Slowly stir in the cornstarch slurry, and continue stirring until the sauce begins to thicken, which should take about 1-2 minutes.
Combine the ingredients: Add the cooked shrimp, steamed broccoli, and water chestnuts to the pan with the sauce. Toss everything together gently to ensure the sauce coats all the ingredients evenly.
Serve and enjoy: Serve the stir-fry hot over steamed rice or noodles, and enjoy your flavorful meal packed with garlic, ginger, and tender shrimp.