Warm the olive oil in a very large frying pan (preferably nonstick) over medium heat. Add the onions and sauté for a few minutes, then add the potato and continue to sauté, stirring occasionally for a few more minutes. Be sure the pan is very warm before you add the eggplant so that it gets a bit brown. Salt and pepper the eggplant, potato and onion mixture.
One ingredient at a time, add the mushrooms, peppers and zucchini, stirring after each addition and adding a bit more salt and pepper.
Turn down the heat a little bit and whisk together the eggs, allspice and water. Add to the pan and stir to scramble the eggs with the vegetables.
When the eggs are almost done, add the tomato and the spinach and stir just enough to wilt the spinach.
Serve immediately with yogurt, cucumber slices, radishes, green onions and pita bread. To eat, break off small pieces of the pita and use them to scoop up the hash.
Note: The potato and the eggplant are diced into smaller pieces so that they cook through; the size of the other vegetables is less important.