Make the garlicky yogurt. In a small bowl, stir together the yogurt, garlic, salt and pepper. Set aside.
Make the spiced butter sauce. Heat a small pan over medium-low heat, and add the butter. Once the butter is melted, add the Aleppo pepper and paprika, and stir for a minute. Turn off the heat.
Prepare the eggs. Crack each egg into a small strainer over a bowl and let the watery egg whites drain, leaving the firmer egg whites around the yolk. After each egg has drained, pour it into a small ramekin.
Make the poached eggs. Heat a medium (and preferably wide) pot of water over medium heat, until simmering. Add the vinegar and stir. Reduce the heat to medium-low, until there's just a few bubbles on the bottom of the pot and gently pour each ramekin with an egg in the water, spaced several inches apart. Cook the eggs for 3 minutes (note: see timing on poached eggs in the notes below). After the eggs have cooked, remove them with a slotted spoon and place then on a paper towel-lined plate.
Make the Turkish eggs. Add the garlicky yogurt to a plate, top with poached eggs, and drizzle the spiced butter sauce on top. Finish with a sprinkle of finely chopped fresh herbs.
