Place the cream, melted butter, minced garlic and salt and pepper into a small bowl or jug. Whisk until combined.
Peel the vegetables, and then chop into very thin slices (approx 3mm thick). Arrange the vegetables in the prepared dish.
Pour over the cream mixture. Check that the vegetables are soft. Cover tightly with foil and bake for 1 hour and 15 minutes.
Remove the foil and sprinkle over the grated cheese. Bake for 15 minutes or until the cheese is bubbling and golden. Allow the vegetable bake to stand for a few minutes before serving.