1. Preheat the broiler. Toss together the tomatoes and oil in a bowl. Season lightly with salt and place on an oiled baking sheet. Slide the baking sheet under the broiler.
  2. Turn the tomatoes continually until all sides are blistered and browned, but not burnt, 4 to 5 minutes. Remove from the oven and set aside. When cool enough to handle, remove the tops and coarsely chop. Reserve the tomatoes and their juice.
  3. Turn off the broiler and preheat the oven to 375ºF.
  4. Warm the butter in a large skillet over medium-low heat for 1 minute. Add the onion and bell pepper and gently cook until very soft, about 3 minutes. Add the garlic and cook until fragrant, about another 30 seconds. Stir in the za’atar, cumin, paprika, and red pepper flakes, and blend completely. Stir in the tomatoes and their juice and season with salt and black pepper. Turn the heat to low and simmer until the tomatoes thicken, about 15 minutes. Stir in the feta.
  5. With a large serving spoon, make 6 indentations in the tomato sauce, evenly spaced around the pan. Gently crack the eggs into the indentations and season the eggs with salt and pepper. Slide the skillet into the oven and bake until the eggs are just set, 5 to 7 minutes. Remove from the oven and sprinkle with the cilantro. Scoop portions from the pan and serve with the pita.
Recipe Notes

NOTE: Za’atar is actually a couple of things. It is, on  one hand, a regional blend of spices (heavy on sumac and thyme) that takes on different flavor profile depending on the locale and the cook blending it. On the other hand, it is a plant from the oregano family. In the Bible it was referred to as hyssop and is mentioned as a medicinal herb and cleanser. It has a delightful flavor or that’s like a cross between the pepperiness of savory, the earthiness of thyme, and the sweetness of rosemary. Recipes for blending your own za’atar are available all over the Internet.