Heat the vegetable oil in a large saute pan over medium heat.

Add the minced shallots and ginger to the pan.

Cover the pan and cook over very low heat until the shallots and ginger are soft, about 10 minutes.

In a small bowl, whisk together the wasabi paste, lime juice, lime zest, salt, and sugar.

Pour the wasabi mixture into the pan with the shallots and ginger.

Stir in the dry white wine and bring the mixture to a simmer.

Add the scrubbed mussels to the pan.

Cover the pan and cook over medium heat until the mussels open, about 8 minutes. Discard any mussels that do not open.

Transfer the opened mussels with a slotted spoon to 4 shallow soup plates, draining them well.

Cover the plates to keep the mussels warm.

Pour the heavy cream into the broth remaining in the pan.

Bring the cream and broth mixture to a slow simmer.

Sift the matcha powder into the pan through a small strainer.

Using a fine whisk or a hand blender, blend the matcha vigorously into the cream and broth mixture until it starts to look frothy and is well combined.

Spoon the matcha broth over the mussels in the soup plates.

Serve immediately.