In a bowl stir together the first four ingredients (through dill). Season with salt and black pepper. Spoon into four shallow dishes. Let stand at least 30 minutes to come to room temperature.
In a small saucepan combine the olive oil, Aleppo pepper, and cumin. Heat over medium just until shimmering, 8 to 10 minutes.
In a 10-inch skillet combine 4 cups water and 1 Tbsp. vinegar. Bring to boiling; reduce heat to simmering (bubbles should begin to break the surface of the water). Break an egg into a cup and slip egg into the simmering water. Repeat with three more eggs, allowing each egg an equal amount of space in the skillet. Simmer eggs, uncovered, 3 to 5 minutes or until the whites are completely set and yolks begin to thicken but are not hard. Using a slotted spoon, remove eggs from skillet.
Add a poached egg to each dish of yogurt. Drizzle with Aleppo oil. Garnish with sprigs of additional parsley and dill. Serve with toast or pita.
