Peel potatoes and cut them into 1/4 inch slices.
Slice off stalk and bottom ends of eggplant. Cut them lengthwise into 1/4 inch slices.
Place eggplant slices in a large bowl filled with salty water and leave to soak for 30 minutes, then remove eggplant from water and leave to dry well on paper towel.⏱ 30 min
Over medium heat, add a 1/4 cup of olive oil to a large frying pan and fry the sliced potato in batches. Make sure to turn them over to cook both sides. The potato slices should be fried until slightly soft, about 4-5 minutes on each side.⏱ 5 min
When the potato slices are cooked, remove from the hot oil and place them on paper towels.
In the same frying pan, add 1/4 cup of olive oil and over a medium heat, start frying the eggplant slices in batches, adding olive oil regularly.
Remove each batch from the hot oil and place them on spread paper towels.
In the same pan, add 1/4 cup oil and sauté the diced onion until translucent. Add ground meat to the onions in the frying pan and mix well to break up the meat.
Stir meat continuously over medium-high heat for 10 minutes.⏱ 10 min
Add red wine, garlic, parsley, salt and pepper to the pan and stir well to mix.
Dilute tomato paste in 1/2 cup of water and add to pan.
Bring to a boil and reduce the heat to medium-low. Simmer uncovered for 30 minutes, stirring occasionally, until liquid is entirely reduced.⏱ 30 min
Grease the sides and bottoms of a baking pan with olive oil.
Cover the bottom completely with a layer of potato slices by overlapping where necessary to ensure a complete covering. Cover with a layer of eggplant slices.
Spoon out a little more than half of the meat mixture and spread to cover the bottom layers evenly.
Cover meat layer with remaining potato slices, then cover completely with another layer of eggplant slices, overlapping as necessary to ensure complete coverage.
Spread remaining meat mixture out evenly to cover the eggplant layer. Using a spatula, press down gently on the layers to compact them.
White Sauce: Melt butter in a medium sized saucepan over a medium-low heat.
When butter is melted, thoroughly incorporate the flour in stages using a whisk and continuously stirring for about 5 minutes.⏱ 5 min
Once the flour is fully incorporated, gradually add the 4 cups of milk while stirring continuously. Turn up the heat slightly to bring the thick sauce to a boil and then remove the saucepan from the heat.
Add nutmeg, salt and pepper and mix sauce well.
Add egg yolks slowly to the sauce, making sure to combine well.
Pour a thick layer of white sauce into baking pan to completely cover the top meat sauce layer. Spread white sauce evenly to ensure a uniform surface.
Place baking pan into an oven preheated to 350 F and bake for 40 minutes or until the top is nicely browned.⏱ 40 min