Fill a small, deep saucepan with about 5 cm of water and bring to a gentle simmer over medium heat. Add a tablespoon of white vinegar to help the egg whites stay together.
While the water heats, crack each egg into a small bowl or ramekin to keep the whites contained and make slipping easier.
Once the water is gently bubbling, create a gentle whirlpool with a spoon to help the whites wrap around the yolk. Carefully slide each egg into the center of the whirlpool, one at a time.
Let the eggs cook for 3-4 minutes until the whites are just set and opaque, with a slightly jiggly yolk. Use a slotted spoon to gently lift each egg out and drain excess water.
Meanwhile, in a small pan, melt the butter over medium heat. Stir in chili flakes and smoked paprika and cook until fragrant, about 30 seconds. Remove from heat.
In a mixing bowl, whisk the Greek yogurt with a pinch of salt, a squeeze of lemon juice if desired, and a drizzle of olive oil until smooth and creamy.
Place a dollop of the seasoned yogurt on each serving plate, spreading slightly to create a bed for the eggs.
Gently place the poached eggs onto the yogurt, keeping the yolks slightly runny for that perfect, golden center.
Pour the warm, spiced butter over the eggs, allowing it to shimmer and soak into the whites.
Garnish with chopped fresh dill or parsley and an extra drizzle of olive oil. Serve immediately with crusty bread or toast if desired.
