In a medium-sized bowl, whisk together Greek yogurt, olive oil, lemon juice, garlic, dill, and salt until creamy and smooth. Set aside.

Fill a saucepan with water and bring to a gentle simmer. Add vinegar, then crack in the eggs and poach for about 3 minutes. Transfer to a paper towel-lined plate.

In a small saucepan, melt butter over low heat. Add Aleppo pepper and stir for about 1 minute until fragrant. Set aside.

Spread equal portions of herbed yogurt in shallow bowls, place poached eggs on top, and drizzle with spiced butter. Garnish with dill or mint leaves.

Serve with crusty bread or pita for dipping.