In a mixing bowl, combine the Greek yogurt, extra virgin olive oil, fresh lemon juice, minced garlic, chopped fresh dill, and sprinkle with kosher salt. Whisk together until smooth and creamy, then set aside.

In a medium pot, fill with water and add the white vinegar, bringing it to a gentle simmer over medium heat. Crack each egg into a bowl and gently slide them into the simmering water, poaching for about 3 minutes.

In a small skillet, melt the unsalted butter over medium-low heat. Add the Aleppo pepper and let cook for about 1 minute until fragrant and bubbly.

On each plate, spread a portion of the herbed yogurt. Using a slotted spoon, lift the poached eggs from the water and place on top of the yogurt. Drizzle with the warm spiced butter sauce.

Serve with warm pita or crusty bread alongside the dish.