Prepare the garlic yogurt base by mixing greek yogurt with minced garlic and salt in a bowl until smooth and well combined. Set aside at room temperature to allow flavors to meld.

Fill a medium saucepan with water and add white vinegar. Bring to a gentle simmer over medium heat - water should have small bubbles but not be at a rolling boil.

While water heats, melt butter in a small skillet over medium-low heat. Add paprika and cayenne pepper, swirling to infuse the butter with color and spice. Remove from heat and keep warm.

Crack each egg into a small ramekin. Create a gentle whirlpool in the simmering water using a wooden spoon, then carefully slide one egg into the center. Repeat with remaining eggs, spacing them apart.

Poach eggs for 3-4 minutes until whites are set but yolks remain runny. Use a slotted spoon to carefully remove eggs, allowing excess water to drain.

To serve, divide garlic yogurt between two shallow bowls, spreading it in an even layer. Place poached eggs on top of yogurt. Drizzle the spiced butter over the eggs and yogurt.

Garnish with additional paprika, black pepper, and fresh dill or parsley. Serve immediately with toasted bread on the side for dipping.