Heat the olive oil in a large, deep nonstick skillet over medium heat.
Add the chopped onion, quartered olives, sweet paprika, ground cumin, and red pepper flakes.
Cook for 2-3 minutes, stirring, until the onion softens and the spices are fragrant.
Add the eggplant cubes to the skillet, tossing to coat them in the spice mixture.
Cover and cook for 4-5 minutes, stirring occasionally, until the eggplant begins to soften.
Stir in the crushed tomatoes, minced garlic, and ¾ cup of water.
Bring the sauce to a gentle simmer.
Cover, reduce the heat, and cook for 10-12 minutes, or until the eggplant is completely tender.
Stir in ¼ cup of the chopped cilantro.
Season with salt and pepper to taste. If the sauce is too thick for your liking, add a tablespoon or two of water to reach the desired consistency.
Using the back of a spoon, create four small wells in the sauce, spacing them evenly apart.
Carefully crack one egg into each well.
Cover the skillet, reduce the heat to medium-low, and simmer for 4-5 minutes, or until the egg whites are opaque and set but the yolks remain runny.
Remove the skillet from the heat and let it stand, still covered, for 1-2 minutes.
Garnish with the remaining fresh cilantro and serve immediately.