Cut the potatoes into quarters, then the quarters into very thin slices (like potato chips).
Pour 1 drop of oil at the bottom of each clay pot.
Distribute the ingredients evenly among them, starting with the potatoes, then meats, crumbled feta cheese, mushrooms, olives and a pinch of savory in each.
Pour on the chopped tomatoes and juice from the mushrooms. You can add a little more water if you'd like it to be runnier, or more tomato juice if you prefer.
Place the clay pots in the oven and turn it on to 392°F (200 °C). Bake about 40 min. Remove the lids and break an egg into each, then return to the oven briefly for the eggs to bake.