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

Fill a medium saucepan with water and add distilled white vinegar. Heat over medium heat until it simmers. Crack the eggs into small bowls, then slide them into the water. Poach for about 3 minutes until the whites are set and yolks are runny.

Using a slotted spoon, gently lift each poached egg out and drain them on a paper towel-lined plate to remove excess moisture.

In a small pan over medium heat, melt unsalted butter until it bubbles. Add Aleppo pepper and cook for another minute until fragrant.

Spread the herbed yogurt in serving bowls, place poached eggs on top, drizzle with spiced butter, and finish with flaky sea salt and black pepper. Serve with warm pita or crusty bread.