Slice eggplants into half an inch wide rings.
Spread the eggplants over a baking sheet and cover with a thin layer of 1 tsp olive oil.
Place in the oven for 10 minutes at 350 degrees fahrenheit (180 celsius), turn eggplants over and place for additional 10 minutes.
In the meantime, fry the onion in the remaining 1 tsp olive oil until clear. Add the garlic.
Add the ground meat to the onion and garlic and cook for another 10 minutes, breaking up the meat from time to time with a spatula.
Add the oregano, thyme, cinnamon, black pepper and tomato paste and mix.
Reduce the heat and cover the pan, cook for 30 minutes, stirring the mixture from time to time.
Add up to ¼ cup of water if becoming dry and sticky.
In a bowl, add the eggs, 1 cup of water, flour and nutmeg and mix.
Once meat and eggplants are ready, start preparing the layers as follows.
Arrange a third of the eggplants as the base.
Cover with half the meat mixture.
Cover with another layer of a third of the eggplants.
Add from above the rest of the meat mixture and finish by covering with the remaining eggplants.
Remix the egg mixture and pour evenly over the eggplants.
Place in the oven for 40 minutes at 350 degrees fahrenheit (180 celsius) or until the egg mixture solidifies.