Preheat oven to 350F/180C/gas mark 4. Spray a pie pan with cooking spray or coat lightly with oil. Or, use a cast iron skillet to make this a one-pan dish.

Put a large sauté pan or cast iron skillet on medium-high heat. Once the pan is hot add oil and swirl to coat. Turn down the heat to medium. Add the veggies as you prep them. (Don't pre-cook the butternut squash.) Stir with each addition. If the veggies start to stick, add a little white wine. They should get golden brown, not too dark.

Add about 3 tablespoons of broth to a small bowl and whisk in the tapioca starch or corn starch until it's a smooth slurry. Heat the rest of the broth in a medium saucepan over medium heat just until bubbling around the edge. Whisk in the slurry and the spices, stirring constantly. Cook for 4 minutes until thickened, then turn heat to low.

When the white potatoes are still firm but almost cooked through, stir all ingredients—except the puréed sweet potatoes—in a large bowl until thoroughly mixed. Pour into prepared pie pan and smooth the top.

Snip off a corner of the sweet potato bag and use corner of bag to pipe sweet potatoes on top as a decorative crust. If using home-cooked sweet potatoes, place in a pastry bag with a large decorative tip. If using a ziptop bag, put all purée in the bag, close the top, then snip the corner. Or use a spatula to spread the potato purée on top.

Bake for 50 minutes until the potato crust is golden brown and you see the gravy bubbling a little through the crust.

Serve immediately.