Probably not exact but should be pretty close, this is a Greek recipe
1 kg potatoes suitable for frying
4 large courgettes
8 medium eggplants
1/2 litre frying oil
For the Sauce
1kg button mushrooms
2 crushed garlic cloves
1 tin chopped tomatoes
2 onions finely sliced
2 tablespoons chopped parsley
2 bay leaves
1/2 cup olive oil
For the Bechamel
1 litre fresh milk
1 cup all-purpose flour
200g grated parmesan cheese (2/3 for the bechamel and 1/3 to sprinkle on top of the bechamel)
Slice the potatoes, courgettes and eggplants lengthwise into 1/2 cm slices
Deep fry them – first the potatoes, then add the eggplants and finally add the courgettes.
Remove them and place them on absorbent kitchen paper to drain off as much oil as possible.
Gently fry the onions in a large pan.
Add the crushed garlic and stir for 1 minute.
Add the mushrooms and continue stirring.
Add the tomatoes and bay leaves.
Add the parsley.
Continue heating until all the juice has been absorbed and you have a thick sauce.
In a heavy-bottomed pan gently heat the butter until it melts.
Add the flour and stir continuously.
Add half of the milk and continue to stir with a whisk.
When the mixture starts to thicken, add the rest of the milk whilst stirring continuously.
When it starts to thicken again, lower the temperature to the minimum and add the grated cheese and then turn off.
In a deep oven dish place a layer with half of the potatoes at the bottom.
Add a layer with the courgettes on top and then a layer with the eggplants.
Spread the sauce on top.
Add a final layer with the remaining potatoes on top of the sauce.
Add the bechamel on top and sprinkle the remaining cheese over it.
Bake in a pre-heated moderate oven for approx. 40 minutes or until it has turned a golden colour on top.