In a large bowl, mix the mash and cabbage until well incorporated. Taste and season with salt and pepper if needed.
Add the oil and butter to a heavy frying pan over medium-high heat. Once the butter is bubbling, add the potato mixture.
Spread the mixture evenly with a spatula, making the surface craggy to ensure it browns. Leave it undisturbed to develop a crust.
You can either flip the mixture in sections until browned on both sides, or transfer the pan to a preheated broiler (grill) to crisp the top. If using the broiler, brush the surface with a little extra melted butter to ensure a deep golden color.