In a small bowl, mix yogurt with garlic and salt. Stir well and let sit at room temperature while you prepare the eggs.
Bring water and vinegar to a gentle simmer in a medium saucepan. Water should have small bubbles but not be boiling vigorously.
Crack an egg into a small bowl. Stir the water to create a gentle vortex, then carefully drop the egg into the center. Poach for about 3 minutes for a runny yolk. Remove with a slotted spoon and drain on a paper towel-lined plate. Repeat with remaining eggs.
Melt butter in a small saucepan over medium heat. Add garlic, paprika, and Aleppo pepper. Cook for about 30 seconds, just until fragrant and slightly frothy. Remove from heat immediately—do not let butter brown.
Divide yogurt evenly between two shallow bowls, spreading it across the bottom. Top each bowl with 2 poached eggs.
Drizzle warm spiced butter over yogurt and eggs. Garnish with chopped parsley or dill.
Serve immediately with warm, crusty bread for dipping.
Notes
Use fresh eggs for cleanest whites and best poached texture
If yogurt is very thick, thin with 1 tablespoon warm water for easier spreading
Don't brown the butter—the goal is a red-hued, fragrant pour, not nutty or dark
Bring yogurt to room temperature before serving for best flavor
To poach multiple eggs at once, use a wider pan and skip the vortex method
Yogurt base can be refrigerated for up to 2 days and spiced butter can be refrigerated for 3-5 days, and rewarmed gently before serving.