In a mixing bowl, whisk together the yogurt, olive oil, and lemon juice until smooth. Then, add the minced garlic, chopped dill, mint, and a pinch of salt. Blend until well combined and set aside.

Fill a medium saucepan with water, add vinegar, and bring to a gentle simmer. Crack the eggs into small bowls and slide them into the simmering water. Poach for about 3 minutes, until the whites are set.

Using a slotted spoon, lift the poached eggs from the water and transfer them to a paper towel-lined plate to absorb excess water.

In a small pan, melt the butter over medium heat, then add Aleppo pepper, stirring to combine as it becomes aromatic.

Spoon the herbed yogurt into shallow bowls, place the poached eggs on top, and drizzle with the spiced butter sauce. Sprinkle with additional herbs if desired.

Serve immediately, accompanied by warm flatbreads or crusty bread.