In a medium mixing bowl, whisk together the yogurt, olive oil, lemon juice, minced garlic, and a pinch of salt. Set it aside.

Fill a medium saucepan with water and add the vinegar. Bring to a simmer.

Carefully crack the eggs into small bowls and slide them into the simmering water. Poach for 3 minutes.

In a small saucepan, melt the butter and stir in Aleppo pepper. Cook until fragrant.

Spread the herbed yogurt on plates, top with poached eggs, drizzle with butter sauce, and garnish.