Prick eggplants several times with a fork.
Place on a glowing grill or hot oven.
Cook for 20 to 25 minutes, turning regularly, until the skin is thoroughly black and the flesh feels soft to the touch.
Remove from grill and allow to cool.
Peel off the skin and mash the flesh with a fork, add lemon juice and set aside.
Melt butter in a pan, add flour and cook for a minute.
Slowly stir in the milk, making sure there are no lumps.
Continue to stir while the sauce comes to a boil and allow to cook for a few minutes.
Take off the heat and stir in the grated cheese, following by the mashed eggplant.
Stir well with a wooden spatula until you have a reasonably smooth mixture.
Fold in the olive oil, adjust seasoning with salt and pepper.