In a large bowl, toss eggplant slices with olive oil and a healthy pinch of Kosher salt, making sure oil is absorbed. Lay eggplant slices single layer on a baking sheet. Roast for about 40 minutes, until eggplant slices are golden. Once cooked, set aside to cool. Turn oven temperature down to 325F.
Meanwhile, make the cream mixture. In a large bowl, whisk together feta, cream cheese, eggs, heavy cream, and black pepper. Beat until the mixture is smooth and thick.
Line the base and sides of a deep 8½ inch square baking pan (or 8 inch diameter pan) with tinfoil. Drizzle with olive oil. Lay cooled eggplant slices into the baking pan. They should lean against each other and almost stand on their sides. Add tomato pieces, filling in the gaps between the eggplants, then top with half the oregano.
Pour cream mixture on top of vegetables, leaving some of the eggplant and tomatoes poking out. Sprinkle remaining oregano and bake for 35-40 minutes, until custard sets and is golden brown. (Mine took closer to 55 minutes). Drizzle with a little bit of olive oil and za'atar to finish.
You can let the cheesecake cool to room temperature, slice it, and serve it that way (the way the recipe was written). Or, you can let it cool just slightly and scoop out warm portions to serve.