I had never really cooked hotdish, but my restaurant entered this moussaka in a local hotdish festival, so I think it qualifies! It’s based on a Turkish version of the dish, with French lentils in place of ground meat.
Preheat the oven to 400˚ F. Char the eggplants over a gas burner, turning with tongs, 4 to 6 minutes. Let cool, then slice 1/2 inch thick.
Arrange the eggplant slices on two baking sheets. Brush with olive oil on both sides and season with salt. Roast until golden and cooked through, 20 to 22 minutes. Set aside.
Combine 6 cups water and the lentils in a large saucepan and bring to a simmer over medium-high heat. Cook until the lentils are tender but not mushy, 10 to 12 minutes. Drain and let cool.
Fill a large wide pot with 1 inch of vegetable oil. Heat over medium-high heat until a deep-fry thermometer registers 350˚ F or a piece of bread dropped in turns golden quickly. Working in batches, fry the potato slices a few at a time until golden but not too brown, 5 to 6 minutes. Remove the potatoes to a rack to drain and season with salt.
Make the lentil-tomato sauce: Melt 4 tablespoons butter in a large wide pot over medium heat. Add the onion and cook, stirring, until softened and starting to brown, about 6 minutes. Add the garlic and cook 1 more minute. Add the cooled lentils and cook for 3 to 4 minutes. Stir in the tomato puree, tomato paste, 1/2 cup water, the oregano, 2 teaspoons salt and 3 grinds of pepper and simmer for 20 minutes. Remove from the heat and set aside.
Make the béchamel: Combine the cinnamon stick, milk and heavy cream in a medium saucepan and bring to a simmer over medium heat; cook 5 minutes. Remove from the heat, stir in the nutmeg and set aside.
In another saucepan, melt the remaining 1 stick butter over medium heat. Whisk in the flour and cook, whisking, 3 to 5 minutes (do not let it brown). Slowly whisk in the heavy cream mixture, bring to a simmer and cook until thick and bubbling, 2 to 3 minutes; remove from the heat. Whisk the eggs in a large bowl, then temper them by whisking in 1 cup of the béchamel; whisk the tempered egg mixture into the remaining béchamel. Season with salt and pepper and add the feta.
Preheat the oven to 350˚ F. Oil an extra-large baking dish or roasting pan. Layer half of the eggplant in the bottom of the pan, then pour half of the lentil-tomato sauce on top, spreading it in an even layer. Top with a layer of half of the potatoes and then spread with half of the béchamel. Repeat the layers (eggplant, lentil-tomato sauce, potatoes, béchamel).
Bake until golden brown, about 30 minutes. (If the top browns too quickly, cover with foil during the last 15 minutes of baking.) Let cool, then cut into pieces.