Heat oil in a cast-iron pan until very hot and smoking
Add oil, onion, garlic, eggplant, mushrooms, and green olives to fry. Add paprika, cayenne, cumin
Add tomatoes and water to the pan
Cover and cook another 10 minutes.
Season well with salt and pepper
Add Feta and stir
Make 4 hollows to place eggs in in the vegetable mixture while in the frying pan
Break an egg into each hollow in the pan.
Cover and simmer for 5 minutes.
Remove from heat. Let stand keeping covered, until the egg whites are set
Before serving sprinkle with basil