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Cut asparagus diagonally into 1 1/2-inch-long pieces.
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Stir together broth, oyster sauce, and rice wine in a small bowl.
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Heat a wok (preferably flat-bottomed) or a 12-inch heavy skillet (not nonstick) over high heat until a drop of water evaporates immediately, then add peanut oil, swirling wok to coat. Add garlic and salt and stir-fry until garlic is fragrant, about 30 seconds. Add asparagus and stir-fry 1 minute.
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Add broth mixture and cook, uncovered, stirring occasionally, until asparagus is crisp-tender, 3 to 6 minutes. Remove from heat and stir in sesame oil.