Sprinkle the slices of eggplant with salt, and let sit for at least half an hour to draw out the bitterness. Rinse off the salt.
Preheat oven to 220C.
Brown the eggplant, zucchini and potato slices in oven for around 10 mins. Remove from pan.
Saute garlic and mushrooms until soft. Add onions and cook until browned. Add vinegar, tomatoes, lentils, half of the canned lentil juice, and oregano. Cover and simmer on medium to low, for about 15 minutes.
Meanwhile, melt butter in a small saucepan Stir in flour and cook gently for a minute or two (no more), stirring frequently
Gradually add the milk, stirring all the time, until sauce begins to boil and then thickens.
Add grated cheese and stir
In a casserole dish (9x13 inches), place a layer of the cooked vegetables, then cheese sauce, then tomato and lentil mixture. Add another layer of vegetables, then sauce. Make sure the top layer is vegetables.
Bake for about 25 minutes.
While it is baking, add nutmeg to the cheese sauce. Remove from heat and let the mixture cool for about 5 minutes. Mix in the beaten egg.
Remove the vegetable portion from the oven and pour on the sauce. Top with parmesan cheese and continue to bake for another 30 minutes.