Prepare the eggplant: Slice eggplant crosswise 1/3 to 1/2 inch thick, discarding the stem and blossom ends. If desired, remove some or all of the skin by stacking 2 or 3 slices and slicing off the skin. Line two jelly-roll or other flat pans with paper towels and lay eggplant slices in a single layer. Salt lightly, then turn over and salt the other side lightly. Set aside to rest for about a half-hour.

Prepare the meat mixture: In a 12-inch skillet or similar pan over medium heat, add the ground beef or lamb and break it up with a spatula. Add the chopped onion; stir and cook, further breaking the meat up into fine pieces, about 10 minutes or until no pink remains. Drain in a fine colander and return to the pan.

Add the allspice, 1/2 teaspoon salt, ground pepper, and tomato sauce to the beef mixture, stirring to combine. Reduce heat and simmer for about 30 minutes.

Bake the eggplant: Preheat the oven to 400° F. When eggplant has rested for 30 minutes, pat the slices dry and remove them from the first pan. Spray the pan with cooking spray and lay the reserved eggplant in a single layer. Spray the tops of the slices with more cooking spray, then bake for 10 to 12 minutes. Remove from oven, turn the slices over, and spray again with cooking spray. Return to the oven to bake for another 4 to 5 minutes. Repeat with the other pan of eggplant slices.

Make the custard: Melt the butter in a 12-inch skillet or similar pan over medium heat. Add the flour and 1/2 teaspoon salt and stir to ensure all flour is evenly coated. Let the mixture bubble and cook for a couple of minutes, then slowly add the milk, stirring constantly. Continue to stir constantly for 5 to 8 minutes, or until mixture begins to boil. Stir and boil for 1 to 2 minutes, then remove from heat and set aside.

Begin layering the moussaka: Spray a 2 1/2 quart baking dish with cooking spray. Layer half the eggplant in the dish, overlapping slightly if needed. Top with half the meat mixture, spreading it evenly, then layer in the rest of the eggplant slices, overlapping if needed. Top with the remaining meat mixture, spreading it evenly.

Finish the custard: Beat the eggs, then add about a half-cup of the warm custard mixture and beat to combine well. Pour the egg mixture into the pan containing the custard mixture, beating or whisking constantly until the mixture is thoroughly combined. Pour the finished custard evenly over the layered eggplant and meat mixture in the baking dish.

Bake: Reduce the oven temp. to 350° F. Bake the moussaka for about 50 minutes, or until the custard is puffed and set and beginning to brown. Remove from the oven and let cool at least 10 minutes before serving. Store leftovers in the refrigerator. Moussaka reheats well; for each serving heat for about 2 1/2 to 3 minutes on the medium setting in the microwave.