Start by adding yogurt to a bowl and whisking it with grated garlic, salt, black pepper, cayenne, and fresh dill. I always let the mixture sit at room temperature so the flavors soften and blend. The yogurt should be smooth, creamy, and well seasoned.
Melt the butter in a small pan over medium heat until it starts to gently bubble. Add Aleppo chili flakes, smoked paprika, and cumin, stirring briefly. Remove from heat once fragrant — the butter should be warm and infused, not burnt.
Bring a saucepan of water to a gentle simmer and stir in the vinegar. Crack each egg into a small bowl, then carefully slide it into the water. Poach for about 2½ to 3 minutes until the whites are set and the yolks remain soft.
Spread the garlic yogurt onto serving plates, creating a smooth base. Place the poached eggs on top using a slotted spoon. Drizzle generously with spiced butter and finish with parsley, dill, or chili oil if using. Serve immediately while warm.