Heat 2 to 3 tablespoons oil in a non-stick or well-seasoned cast iron skillet over medium or medium-high heat, until the oil is hot enough that a potato sizzles when it touches it.
Add the potatoes, along with 1/4 teaspoon salt (or to taste). Spread them out evenly over the bottom of the skillet, and let them sit for a couple minutes before stirring them. Stir every couple minutes for about 15 to 20 minutes, until the potatoes are golden brown and cooked through. Once they’re done, remove from heat and stir in the za’atar.
While you wait on the potatoes, whisk together the yogurt, tahini, lemon juice, water, and a pinch of salt, until it’s totally smooth.
Also while you wait, fry your eggs however you like. Here’s how I do it: Heat a small skillet over high heat for at least 3 minutes, until it’s very hot. Add about 1 or 2 tablespoons of oil to the pan, swirl it around, and immediately crack an egg wherever the oil is pooling. Be very careful—it will splatter violently. While the egg is cooking, season it with some salt and (carefully!) baste it by spooning hot oil onto the whites to help them cook faster. The egg is done once the whites are set and brown on the bottom and around the edges (just about 2 minutes). Remove to a plate and repeat if you’re making multiple servings (replace some of the oil as you go) (eggs inspired by Smitten Kitchen).
Once the eggs are done, remove them to a plate, pour off the old oil, replace with a teaspoon of new oil, and add the spinach leaves and a pinch of salt. Keep over high heat to wilt the spinach (stir it constantly for about 2 to 3 minutes, until it’s bright green and wilted). Most of the liquid should cook off, but if the spinach looks watery after 3 minutes, wring it out with the back of a spoon and strain away the liquid.
Combine the spinach with the potatoes, stir everything together, top with the yogurt sauce, crispy eggs, green onions, and a little extra za’atar, and serve.