In a medium bowl, gently combine the diced king oyster mushrooms, diced lychee, chives, cilantro, and shallot.
Set aside.
To make the aioli, combine the aquafaba and mustard in a separate, clean bowl.
Using an immersion blender or a whisk, blend until frothy.
Very slowly, drop by drop at first, begin to drizzle in the vanilla oil while continuously blending or whisking. As the mixture starts to thicken and emulsify, you can pour the oil in a thin, steady stream.
Continue until it reaches a light mayonnaise consistency.
Whisk in the sherry vinegar.
Gently fold the vanilla aioli into the mushroom and lychee mixture until everything is well coated.
Season generously with salt and freshly ground black pepper to taste.
For the best flavor and texture, serve immediately, ice-cold. Spoon into mini martini glasses or onto appetizer spoons.
Chill your serving glasses in the freezer for 15-20 minutes before plating. This keeps the tartare perfectly cold and refreshing from the first bite to the last.