Parboil the sweet potatoes and potatoes in a large saucepan of salted, boiling water until tender to the point of a knife, about 15 minutes.
In the meantime, prepare the crumble by combining the flour, butter, Cheddar, and rosemary in a food processor.
Pulse together until the mixture resembles breadcrumbs. Alternatively, you can rub the ingredients together with your fingertips in a mixing bowl.
Grease an oval baking dish with olive oil. Arrange the sweet potato, potato, and cod in the dish, in layers, seasoning between the layers with salt and pepper. Spoon the savoury crumble on top.
Bake until golden-brown on top, about 30-40 minutes. Remove from the oven and top with crumbled Chavroux goat’s cheese, serving warm.