Preheat the oven to 350°F.
Wash and peel the cassava, then cut into approximately 2-inch pieces.
Add the cassava to lightly salted boiling water with the vinegar. Cook until tender.
Drain the cooked cassava and allow it to cool enough to handle. Remove the tough inner strings, then roughly cut the cassava into cubes.
Cook the codfish in a shallow pan with a small amount of lightly salted water until tender and it flakes easily. Remove from the water, allow to cool slightly, then flake the fish, checking for any bones.
Melt the butter with the olive oil in a pan over medium heat. Add the onions, garlic, Scotch bonnet, chives, thyme, and sweet peppers. Sauté until softened and fragrant.
Add the flaked codfish to the sautéed seasonings and gently combine. Sprinkle in the cornstarch and stir until the fish mixture thickens slightly.
Add the cooked cassava and white pepper to the fish mixture. Gently combine, allowing some of the tender cassava to break down without mashing it smooth. Taste and adjust the salt and pepper as needed.
Transfer the cassava and fish mixture to a buttered baking dish. Spread evenly and sprinkle the grated cheese over the top.
Bake for 10 to 15 minutes, or until heated through and the cheese is melted and lightly golden.