Prepare all the ingredients ahead of time.
In a small bowl, mix together the soy sauce, brown sugar, oyster sauce, and water to make the sauce. Set aside.
Cook the noodles according to the package instructions, and then drain them. Set aside.
In a wok or large pan, heat 1 Tbsp of vegetable oil over medium-high heat. Sauté the shrimp in batches until they are cooked through. Remove the cooked shrimp from the pan and set aside.
Add another 1-2 Tbsp of vegetable oil to the same pan. Stir-fry the onions, carrots, and celery for 2-3 minutes until they become slightly tender but still have a crunch. Add the shredded cabbage and minced garlic to the pan and continue to cook for another 1-2 minutes.
Pour the prepared sauce over the vegetables in the pan. Add the cooked noodles and the sauteed shrimp. Bring everything to a simmer, tossing occasionally to ensure everything is coated in the sauce.
Once the noodles are well-coated and heated through, remove the pan from the heat.
Garnish the shrimp chow mein with chopped green onions.