Preheat oven to 400F
Add the sliced potatoes and onions to a bowl with a sprinkle of salt, pepper, 1 Tablespoon oregano, and 1 tablespoon oil. Keep this bowl handy for the remaining vegetables. Place the potatoes evenly on a 9×13 baking dish and roast for 35 minutes or until they begin to soften and become golden.
While the potatoes are roasting, prepare your meat filling. Add the oil to a large pan over medium heat. Add the meat and cook down, breaking apart the larger chunks as much as possible. Once the meat is halfway cooked through, add the diced onions, and garlic. Cook until onions are softened and garlic is fragrant. Add in the allspice, oregano, salt and pepper and cook for another 30 seconds. Add in the tomato paste and can of diced tomatoes and let it cook down for about 10 minutes or until some of the liquid has evaporated. Remove from heat and set aside.
When the potatoes are done, remove the tray from the oven and mix together the eggplant, olive oil, salt, pepper and 1 tablespoon oregano in the same bowl. Place the eggplant slices on top of the roasted potatoes in one even layer and bake for an additional 20 minutes.
While the eggplant is in then oven, work on the béchamel sauce. Add the butter to a saucepan over medium heat. Once it's melted, add in the flour and whisk to combine until a thick paste is formed and flour is cooked through. Slowly start adding in the milk about ½ cup at a time to ensure that it is fully incorporated. Keep adding the milk and whisking from the bottom until it is thick and creamy and begins to bubble slightly. Lift your whisk and you should see ribbons of béchamel falling on itself in the pot. This means the consistency is right and the sauce is done. Turn off the heat, add nutmeg, some salt, pepper and set aside.
Pull out the tray, mix together the zucchini, olive oil, salt, pepper and 1 tablespoon oregano in the same bowl . Place the zucchini slices on top of the roasted eggplant and bake for an additional 15-20 minutes.
In the 9×13 pan on top of the veggies, evenly spread the meat mixture and with the back of a spoon. Gently pour half the béchamel sauce on top of the meat and spread carefully to cover all the surface area. Pour over the rest of the sauce and spread evenly. Sprinkle or grate on the parmesan cheese and place back into the oven for 20 minutes and broil for 3-4 minutes or until the top begins to turn golden brown. Remove from oven and let it set for about 30 minutes (similar to a lasagna, you want to let this dish set so when you’re slicing it, everything stays intact and it doesn’t spill all over the tray) and enjoy!