Rinse the eggplant, zucchini and potato in cold water, then pat dry.

Heat a drizzle of olive oil in a large heavy-based saucepan over low–medium heat.

Add the onion and cook for 6–8 minutes or until translucent.

Add the mince to the pan, stirring to break up any clumps, then cook for 8–10 minutes or until browned all over.

Add the tomato, tomato paste, spring onion, parsley and mint and stir to combine, then season to taste with salt and pepper.

Bring to a simmer over medium heat, then reduce the heat to low and cook for 25 minutes or until thickened.

Meanwhile, heat olive oil for shallow frying in a frying pan over medium heat.

Working in batches, cook the eggplant for 2–3 minutes on each side or until golden brown. Transfer to a plate lined with paper towel and set aside to drain.

Cook the zucchini for 2–3 minutes on each side or until golden brown, then transfer to a plate lined with paper towel and set aside to drain.

Cook the potato for 3–4 minutes on each side or until golden brown, then transfer to a plate lined with paper towel and set aside to drain.

To make the sauce, heat the milk in a heavy-based saucepan over medium until it is almost boiling.

Melt the butter with the oil in a separate heavy-based saucepan over medium heat, then stir in the flour and cook for 2 minutes or until combined to form a paste.

Gradually add the hot milk, stirring continuously with a whisk or large metal spoon to prevent lumps forming, until all the milk is incorporated and the mixture is thick and smooth.

Remove from the heat and set aside to cool slightly.

Add the nutmeg, then whisk in the egg until well combined.

Preheat the oven to 180˚C.

Place all the meat mixture in a 3.75 litre baking dish, then layer with the eggplant, zucchini and potato.

Top evenly with the sauce and sprinkle with grated cheese.

Place the baking dish on a baking tray to catch any overflowing juices, then bake for 45 minutes–1 hour or until golden and bubbling.

Cut into slices and serve.