In a large sauté pan, heat the oil over medium-high heat. Add the onion and sauté until translucent, about 5 minutes. Add the garlic and herbs, if using, and cook for 2 minutes longer. Stir in the spinach and kale and sauté until softened, about 3 minutes. Add the chickpeas, lemon juice, za’atar, 1 teaspoon salt, and 1/2 teaspoon black pepper, and toss all together. Taste and adjust the seasoning to your liking.
Reduce the heat to low and bring the mixture to a simmer. Place a few mounds of cheese over the top of the greens. Use a wooden spoon to form 6 craters (indentations) in the greens; this is where the cracked eggs will be dropped. Working with one egg at a time, crack an egg into a small bowl (to catch any loose shells), and then pour it into the crater. Repeat with the remaining eggs. Raise the heat to medium, cover the sauté pan, and cook for 4 minutes. Uncover and cook for a few minutes longer, depending on the doneness of the eggs. The goal is to have the whites slightly firm but the yolks still runny. Remove from the heat, drizzle with extra-virgin olive oil, and sprinkle with red pepper flakes. Serve right away.
Make-Ahead Tip: The greens and chickpeas can be kept in the sauté pan on the counter for up to 2 hours until ready to reheat and add the cheese and eggs.