In a medium bowl, combine the Greek yogurt, grated garlic, black pepper, salt, cayenne, and chopped dill.
Mix well until smooth and creamy.
Let the yogurt sit at room temperature while preparing the remaining ingredients.
In a small saucepan, melt the butter over medium heat.
Once melted and lightly bubbling, stir in the Aleppo pepper, smoked paprika, and cumin.
Remove from the heat and allow the spices to infuse for several minutes.
For the optional herb oil, combine parsley, jalapeño, olive oil, and salt until well mixed.
Bring a saucepan filled with 2–3 inches of water to a gentle simmer.
Add the vinegar.
Crack each egg into a small bowl before gently sliding it into the water.
Poach the eggs for 2½–3 minutes, or until the whites are set and the yolks remain soft.
Remove the eggs with a slotted spoon and gently pat dry.
Spread the yogurt mixture onto serving plates, creating shallow ridges with the back of a spoon.
Drizzle with the parsley jalapeño oil if using.
Place two poached eggs on each plate.
Spoon the warm Aleppo butter generously over the eggs.
Finish with a pinch of flaky sea salt and serve immediately with warm bread.