Pat vegan barramundi fillets dry.
Brush fillets with olive oil, salt, and pepper; set aside.
In a saucepan, whisk soy sauce, ginger, garlic, sugar, vinegar, and sesame oil.
Simmer 3 minutes, stir in cornstarch slurry, and cook until thickened.
Preheat grill to medium-high; oil grates lightly.
Grill fillets 6–7 minutes per side until charred and tender.
Brush ginger soy sauce over fillets during final minute.
Remove from grill, drizzle extra sauce, and serve hot.