In a small bowl, whisk together the Greek yogurt, minced garlic, and a pinch of the sea salt, then set aside to reach room temperature.
Fill a medium saucepan with water, add the white vinegar, and bring to a very gentle simmer over medium heat.
Crack each egg into a small ramekin and carefully slide them into the simmering water one at a time.
Poach the eggs for approximately 3 to 4 minutes until the whites are fully opaque and set, but the yolks are still soft.
While the eggs are poaching, melt the ghee in a small skillet over medium-low heat until shimmering.
Stir the Aleppo pepper and smoked paprika into the melted ghee, cooking for 30 seconds until the oil turns a deep red and smells toasted.
Spread the room-temperature garlic yogurt in a thick layer across the bottom of a shallow serving bowl.
Use a slotted spoon to remove the poached eggs from the water, dabbing them briefly on a paper towel to remove excess moisture.
Place the poached eggs gently on top of the yogurt bed.
Pour the warm chili ghee over the eggs and yogurt, then garnish with fresh chopped dill, the remaining sea salt, and black pepper.