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In a small bowl, mix the shrimp with 1 teaspoon of soy sauce, 1 teaspoon of sesame oil, and the cornstarch. Let it marinate for about 10-15 minutes.
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Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the shrimp and stir-fry until they turn pink and are just cooked through, about 2-3 minutes. Remove the shrimp from the skillet and set aside.
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In the same skillet, add a bit more oil if necessary. Add the garlic and ginger, and stir-fry for about 30 seconds until fragrant.
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Add the chopped bok choy and stir-fry for about 2-3 minutes until it starts to wilt. If you like it more tender, cook a bit longer.
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Return the shrimp to the skillet. Add the remaining soy sauce, oyster sauce, and chicken broth (or water). Stir to combine all the ingredients.
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Cook for another 1-2 minutes until everything is heated through and the sauce thickens slightly.
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Drizzle the remaining sesame oil over the stir-fry.
Season with salt, pepper, and red pepper flakes if using.
Serve hot over steamed rice or noodles.