Heat the coconut oil into a cast-iron skillet, add the diced onion and fry until translucent.
Add the diced tomatoes, purified water, vinegar, sugar, cumin powder and salt, mix to combine, bring to boil and let simmer over low heat until thickened.
Prepare the zhoug meanwhile - place all the ingredients except oil into a food processor and pulse to form a chunky paste. Add the oil gradually and process to obtain a pesto-like consistence.
Crack the eggs on top of the sauce and cover the skillet with a lid.
Cook over low heat until the egg whites are set and the yolks are a bit cooked, but still runny.
Remove the lid, drizzle with zhoug and serve warm as it is or with hummus.