Point to note:
Most Aubergines will taste VERY bitter until "cured". If you've ever tried them and found them rather "tart" they won't have been sorted.
With that in mind, papoutsakia ("little shoes"):
Take each aubergine and split it in half (along the length so you get 2x shoe/boat shaped pieces).
Salt the fleshy surface and submerge in water for about... 1-3 hours (you'll have to experiment a bit). This leeches most of the bitterness out of them.
Either fry them, flesh side down in a little oil or stick them in the oven flesh side up until the flesh softens (for the oven it's about 40 minutes, I forget for the pan method, we've used the oven way for ages).
Take them out, mash the fleshy surface down a little to make a dish/bowl (careful not to pierce the skin).
Make up a batch of meat sauce (It's basically the Greek version of Bolognese. Soften onion, preferable a red one, in a pan, add finely diced/pressed garlic, then add mince until browned, then add wine until it's mostly evaporated, then add tinned tomatoes, salt, pepper, oregano, cinnamon, maybe a tiny pinch of cloves too).
Make up a batch of béchamel (flour and butter to make a paste, slowly add splashes of warm milk until you get a sauce texture, allow to cool a bit and add egg yolks for more flavour)
Grate a decent amount of hard cheese.
So you basically take your boats, spoon in the mince, top off with the béchamel, throw grated cheese on top and stick in the oven for about 20 minutes at 180c.
Similar recipe
here, mines from memory (as taught by my Greek wife).