Place the dried shrimp in a small bowl and pour 1/2 cup of warm water over them, allowing them to soak for 15 minutes to soften. Drain the shrimp, reserving the soaking liquid for later use.

Wash the Napa cabbage thoroughly and separate the leafy green parts from the thick white stems, cutting both into 2-inch pieces while keeping them in separate piles.

Heat the cooking oil in a large wok or skillet over medium heat. Add the minced garlic and the drained dried shrimp, stirring constantly until the garlic is golden and fragrant, about 1 to 2 minutes.

Increase the heat to high and add the thick white cabbage stems to the wok. Stir-fry for 2 to 3 minutes until the stems start to soften slightly and turn translucent around the edges.

Add the green cabbage leaves to the wok, then pour in the reserved shrimp soaking liquid, oyster sauce, and soy sauce. Toss well to combine all ingredients and evenly coat the cabbage.

Cover the wok with a lid and let it steam over medium-high heat for 3 to 4 minutes, or until the cabbage is tender but still retains a slight bite.

Remove the lid, stir in the sesame oil, and cook for another 1 minute until the sauce reduces slightly and clings to the cabbage before serving hot.