Preheat your oven to 400°F (200°C).
In a mixing bowl, combine the mayonnaise, soy sauce, sake, sesame oil, sugar, and black pepper. Mix well until smooth.
Stir in the chopped green onions and mozzarella cheese until evenly combined.
Place the shucked oysters on a baking sheet, making sure they are stable and not tipping over.
Spoon a generous amount of the mayonnaise mixture onto each oyster.
Sprinkle panko breadcrumbs evenly over the top of each oyster for added crunch.
Bake in the preheated oven for about 10-12 minutes, or until the topping is golden and bubbly.
Remove from the oven and let cool slightly before serving. Garnish with chopped parsley.