
Get your egg poaching water ready. Bring a medium pot of water to a steady simmer over medium-low heat.
Meanwhile, soften the sweet potatoes. In a 12-inch cast-iron skillet, heat the olive oil over medium-high heat until shimmering but not smoking. Add the red onion, sweet potatoes, and chickpeas. Season with a big pinch of salt and black pepper (about 1/2 teaspoon each). Add the coriander, cumin, paprika, and turmeric. Stir to combine. Cook, stirring frequently, until the onion is nicely caramelized and the sweet potatoes have softened quite a bit, 10 to 15 minutes.
Build the flavor. Reduce the heat to medium, then stir in the garlic and bell pepper. Continue to cook, stirring frequently, until the pepper has softened and the potatoes are now cooked through, another 5 to 10 minutes. Sprinkle with the za’atar.
Poach the eggs. Add the vinegar into the pot with the simmering water. Break each egg into a small bowl or ramekin. Stir the simmering water gently and carefully slide each egg in; the egg whites should wrap around the yolk. Cook for 3 minutes exactly, then use a slotted spoon to transfer the eggs to a paper towel to drain. Season with a pinch of salt, pepper and a little more za’atar.
Finish and serve. Divide the sweet potato hash among 4 bowls and top each with a poached egg. Serve immediately.