Bring a medium pot of water to a gentle simmer. Add a tablespoon of vinegar (optional) to help the eggs hold their shape. Crack each egg into a small bowl and gently slide them into the simmering water. Poach the eggs for about 3-4 minutes until the whites are set but the yolks are still runny. Use a slotted spoon to transfer the poached eggs to a paper towel-lined plate to drain.

While the eggs are poaching, mix 1 cup of Greek yogurt with the minced garlic, fresh dill, fresh mint, lemon juice, salt, and pepper to taste. Spread the yogurt mixture evenly on a serving plate.

In a small saucepan, melt the unsalted butter with the extra-virgin olive oil over medium heat. Once the butter starts to foam, add the Aleppo pepper and paprika. Stir for about 1 minute until the spices are fragrant and the butter turns a deep red color. Remove from heat.

Place the poached eggs on top of the yogurt mixture. Drizzle the spiced butter over the eggs and yogurt. Sprinkle with crumbled feta cheese and garnish with fresh herbs. Serve immediately with toasted sourdough bread on the side for dipping.