About an hour in advance of cooking, peel and slice your eggplant into very thin slices. Layer the slices in a bowl, sprinkling each layer with salt, then let it rest for an hour.
When your hour is close to being up, you can start to brown the beef. While that's cooking, drain your eggplant slices in a colander and rinse them well. Lay them out in a single layer on a broiler-safe pan (I use a cast iron skillet) and brush them with plenty of extra virgin olive oil. Broil them until they're slightly browned (8 minutes for me, but your mileage may vary).
Meanwhile, once your beef has browned, add the onion, tomatoes, stock, cinnamon, and salt and simmer it all until most of your liquid has evaporated.
Brush a casserole dish (I use a 9-inch round dish) with extra virgin olive oil and put down a layer of eggplant slices. Top that with a layer of the beef/tomato mixture and repeat this process until you have no layers left. Top with the grated cheese and bake at 350 degrees for 20-25 minutes (or until cheese starts to turn golden).