Rinse and scrub the mussels under cold water, changing the water several times, to remove any grit. Debeard the mussels by removing the stringy bits in the seam where the two shells meet as best you can. Discard any mussels with cracked shells or any with open shells that don’t close when you gently tap them against the counter.
Heat a wok or large skillet over medium-high heat until a bead of water sizzles and evaporates. Add the oil and swirl to coat the base. Add the ginger and shallots and stir-fry until aromatic, about 30 to 40 seconds. Add the rice wine and fish sauce . Carefully add the mussels and cover with a lid. Allow the mussels to steam for 5 minutes, then uncover. Stir in the white pepper.
Discard any mussels that have not opened, then transfer to a serving dish along with the broth remaining in the pan. Sprinkle the scallions on top and serve.