Preheat oven to 375 . In a large bowl, toss eggplant with 1 tbsp oil, salt, paprika, and cumin. Lay on a sheet pan and bake for 20 minutes.
In the meantime, heat 1 tbsp oil in a cast iron skillet. Season sliced mushrooms with salt and pepper, then sauté 5-7 minutes until edges are brown. Set mushrooms aside.
Heat final tbsp of olive in the cast iron skillet. Sauté onion until transparent. Add tomato, paprika, cumin, and red pepper flakes, cooking for 10 minutes until thickened and fragrant. Add mushrooms and eggplant to sauce, then taste for seasoning.
Make a well in the sauce for each of the eggs. Crack the eggs into the wells, then add mozzarella balls throughout. Poach on stove top or in the oven until eggs have reached the desired doneness. Watch carefully— the bottoms cook before the tops look done. The yolk should be runny with a fully set but soft white. Serve with crusty bread.