In a small bowl, mix together the Greek yogurt and minced garlic. Season with salt and pepper to taste. This creamy yogurt mixture will be the perfect base for your Turkish eggs.
Fill a medium-sized saucepan with water and bring it to a gentle simmer over medium heat. While the water is heating up, crack each egg into a small cup or ramekin.
Once the water is simmering, carefully slide each egg into the water, one at a time. Poach the eggs for about 3-4 minutes for soft, runny yolks, or longer if you prefer firmer yolks.
While the eggs are poaching, melt the butter in a small skillet over medium heat. Once melted, add the olive oil and paprika, and stir to combine. This spiced butter will add a burst of flavor to your Turkish eggs.
Once the eggs are cooked to your liking, carefully remove them from the water using a slotted spoon and place them on a plate lined with paper towels to drain any excess water.
To assemble the Turkish eggs, spread a generous dollop of the garlic yogurt mixture onto each serving plate. Carefully place the poached eggs on top of the yogurt.
Drizzle the spiced butter mixture over the eggs and yogurt. Garnish with chopped fresh herbs, such as parsley or dill, for a pop of color and freshness. If you like a bit of heat, sprinkle some chili flakes or drizzle with chili oil.
Serve your Turkish eggs immediately, accompanied by crusty bread or toasted pita for dipping into the creamy yogurt and runny yolks.