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

Fill a medium saucepan with approximately three inches of water and add distilled white vinegar. Heat until just below a simmer. Crack two large eggs into ramekins and slide them into the water. Poach for about 3 minutes.

Using a slotted spoon, lift the poached eggs out of the water and allow excess moisture to drain. Transfer to a paper towel-lined plate.

In a small skillet, melt unsalted butter over medium heat until frothy. Add Aleppo pepper and sauté for about 1 minute until fragrant.

Spread herbed yogurt across shallow bowls. Nestle poached eggs atop yogurt, drizzle with spiced butter, and garnish with dill or mint. Serve immediately with pita or crusty bread.