In a mixing bowl, combine whole milk Greek yogurt, extra virgin olive oil, lemon juice, grated garlic, chopped fresh dill, and kosher salt. Whisk until smooth and creamy, then set aside.

Fill a saucepan with water and bring to a gentle simmer. Stir in distilled white vinegar. Crack eggs into ramekins and carefully slide each into the simmering water. Poach for about 3 minutes until whites are firm but yolks remain soft.

Using a slotted spoon, lift the poached eggs out and place them on a paper towel-lined plate. Let them rest while preparing the next component.

In a small saucepan, melt unsalted butter over medium heat until bubbling. Stir in Aleppo pepper, letting it infuse for about 1 minute until fragrant.

In shallow bowls, spoon the herbed yogurt as the base. Place two poached eggs on top, drizzle with warm butter sauce, and season with flaky sea salt and black pepper to taste. Garnish with additional herbs if desired.