Stir yogurt, dill, garlic, salt, and pepper in a bowl. Divide between 2 plates and set aside.
Boil a vessel of salted water. Reduce heat to medium and add vinegar; using a slotted spoon, swirl water to create a whirlpool. Crack 1 egg at a time into a bowl and slide egg into water; poach until white is firm but yolk is still runny, about 3 minutes. Using slotted spoon, transfer eggs to paper towels to drain; divide between plates.
Melt butter in an 8" skillet over medium-high heat. Stir in some garlic, parika and salt; drizzle over eggs.