Preheat oven to 400 degrees. Place lingcod in baking dish; rub with 1 Tbsp. oil. Roast fish in oven until cooked through, 15–20 minutes, depending on thickness.
Let cool completely, then pat dry with paper towel. Flake with fork, not too fine; leave some larger pieces for texture.
In a large bowl, combine fish, egg, green onions, mayonnaise, lemon juice, mustard, bread crumbs, parsley, hot sauce, salt, and pepper. Fold gently until ingredients just hold together. Form into eight equal-size cakes.
Heat 1 Tbsp. oil in large nonstick skillet over medium heat. Cook cakes until golden brown, about 2 minutes on each side. Serve hot.
Beverage pairing: red ale or Chardonnay