Peel and slice the potatoes and eggplants fairly thin. Lightly oil a baking pan, add a layer of potatoes or eggplants, sprinkle lightly with salt, drizzle with a little oil, and toss to coat. Bake everything at 430°F (220°C) for 10-15 minutes for the potatoes and about 10 minutes or less for the eggplants.

Prepare the béchamel. In a pot, heat most of the milk. Reserve a little in a bowl to mix with the flour and semolina until smooth. Once the milk is hot, add the flour mixture, stirring constantly. When it thickens, remove from heat and add the egg and butter, plus a pinch of salt. Spread a little béchamel on the bottom of your baking dish.

Continue layering with potatoes, meat sauce, and eggplants. (I put only potatoes in one corner because my husband doesn’t eat eggplant.)

Add another layer of meat sauce, feta, potatoes, and the rest of the meat sauce.