Prepare the Yogurt Base: In a medium bowl, combine the Greek yogurt, grated garlic, lemon zest, lemon juice, ground sumac, and a pinch of kosher salt. Stir well until smooth and fully incorporated. Set aside to allow flavors to meld.

Create the Warm Chili Oil: In a small bowl, whisk together the 3 tablespoons of olive oil designated for the spice oil, the red pepper flakes, sweet paprika, smoked paprika, cayenne pepper (if using), and the 3/4 teaspoon kosher salt. Set this mixture aside.

Mix the Za'atar Infusion: In a separate small bowl, stir together 2 tablespoons of the remaining olive oil with the 2 rounded teaspoons of za'atar spice blend.

Cook the Eggs: Heat the final 2 tablespoons of olive oil in a non-stick skillet over medium heat. Once the oil shimmers slightly, gently crack the 3 eggs into the skillet, ensuring they don't crowd. Cook the eggs according to your preference – sunny-side up or gently flipped over-easy are recommended to keep the yolks runny. Season the eggs lightly with salt while they cook.

Assemble the Dish: Divide the prepared Lemony Sumac Yogurt evenly among three individual shallow bowls or plates, spreading it to create a base. Carefully transfer one cooked egg onto the yogurt base in each bowl.

Garnish and Serve: Drizzle the za'atar oil mixture over the eggs and the surrounding yogurt. Sprinkle generously with the mixed fresh herbs and the chopped fresh mint. Finally, spoon the warm chili oil over the dish, adding as much or as little as desired. Serve immediately with warm pita, naan, or crusty bread for dipping.