In a medium bowl, whisk together Greek yogurt, extra virgin olive oil, fresh lemon juice, minced garlic, fresh dill, and kosher salt until velvety and smooth. Set aside at room temperature.

In a medium saucepan, bring water to a gentle simmer over medium heat, adding distilled white vinegar. Crack the eggs into small bowls. Carefully slide each egg into the simmering water and poach for about 3 minutes. Remove using a slotted spoon and drain on paper towels.

In a small skillet, melt unsalted butter over medium heat until frothy. Stir in Aleppo pepper and allow it to sizzle gently for about 1 minute. This will enhance the rich flavors of the dish.

On shallow plates, spread the herbed yogurt mixture. Place two poached eggs on each plate and drizzle with the spiced butter. Garnish with fresh herbs and a sprinkle of flaky salt. Serve with pita or crusty bread.