In a large clean saucepan (you can clean the one you used to make the stock), drizzle the oil to coat the bottom. Layer the tomato slices on the bottom, this will help keep the rice from sticking.
Arrange the eggplant slices evenly around the pan, coming up the sides of the pan if you can so that they'll sort of end up wrapping the rice mixture (see video below for clarification).
Sprinkle the eggplants with salt, and add all the meat cubes to the pan. Add the chickpeas on top of the meat. Add half the rice and spread it out evenly. Add the cooked potato slices and half the cauliflower florets. Season these vegetables with a sprinkle of salt.
Add the second half of the rice on top of the vegetables, and pat with the pack of a wooden spoon to firmly press it into the pan.
Pour the meat stock over the rice. It should cover the top of the rice by about 1/2 inch. If you need to, add a little water in order to submerge the rice, maybe 1/2 cup or so. Place the pot of rice on medium high heat until the water in it comes to a boil, about 5 minutes or so, then tightly cover (if your lid doesn't fit tightly, you can place a kitchen towel under the lid before covering).
Reduce heat to low, and cook for 50-55 minutes, until all the broth has been absorbed and the rice is fluffy. Remove from heat and let the pot stand for 5-10 minutes.
After the rice has rested, remove the lid and place a serving platter or tray on top of the pot. Flip the pot upside down, but don't lift the pot up for a few minutes to give the rice time to drop. After a few minutes pass, slowly use the pot handles to lift and remove the pot.
Garnish your makloubeh with plenty of toasted nuts and parsley. Enjoy immediately! We like this with yogurt and/or a simple green salad.