Preheat the oven to 175 C.
Being by preparing the aubergines: roughly peel them leaving small strips of the skin then slice them thinly lengthways (around 1 cm thick). Lightly salt them in both sides and place them in a colander for an hour until their natural water is drained a little.
Meanwhile slice the courgettes lengthways (1 cm thick) and peel and slice the potatoes as thin as you can using a mandoline. (Place the potatoes in a bowl of cold water until ready to use to prevent browning).
Place the potatoes next to the aubergines on a large paper lined baking tray and drizzle some olive oil on both sides and season with salt and pepper and place in the oven. Roast for 15-20 minutes or until golden and soft. (You may need two trays to fit them all in)
Do the same with the courgette - place them in a paper lined baking tray and drizzle a little olive oil on both sides and season with salt and pepper and roast for 15 minutes.
Meanwhile add your puy lentils to a pot of boiling water and cover on low/medium heat for 10 minutes then add the brown lentils in and cover for another 10 minutes. When the lentils are soft but not mashed take them out and drain the water.
Heat 2 tablespoons of olive oil in a large frying pan and saute the onions until they are soft and a little brown at the edges ( about 5 minute), then add the crushed garlic, cinnamon and thyme and saute for 1 minute. Add the tomato paste and saute for 2 minutes followed by the chopped tomato (pommi).
Season with 1 teaspoon of salt and 1/4 crushed black pepper and simmer on low heat for 15 minutes. Then add the drained lentils and mix gently. Leave it on low heat for 10 minutes stirring occasionally until most of the sauce has reduced. Turn off heat and set aside.
Now for the bechamel: In a large pot heat the butter on medium/low heat until melted and add the flour while constantly mixing. Then add your milk one ladle at a time while constantly mixing - taking a 1 minute break after each ladle so as the milk is absorbed.
Once all the milk is in use a whisk and continue whisking until the sauce thickens. Season with salt, pepper and nutmeg. Once the bechamel starts to bubble then it's ready. Turn the heat off and set aside to cool a little.
Stir in the parmesan and mix well then add the egg yolks and mix as well.
Finally, brush a little oil onto a glass baking dish and layer the eggplants. Layer the courgette on top followed by the potato. Add the lentil - tomato mixture on top and flatten well. Pour the creamy bechamel all over and add a little parmesan cheese on the top.
Bake at 175C for 40 minutes or until golden brown and bubbling.