Heat oil in a medium skillet over medium heat. Stir in garlic and brown sugar, and cook until garlic is lightly browned. Stir in green onions, and cook until tender. Mix in oyster sauce and water.

Place salmon fillets into skillet, and reduce heat to medium low. Spoon sauce mixture over fillets. Cook 10 to 15 minutes, until fish is easily flaked with a fork.

Remove fish from skillet, and set aside. Mix cornstarch and warm water into the remaining sauce mixture. Stir until thickened to desired consistency. Pour over salmon to serve.