1. Combine yogurt, garlic, and chives in a small bowl. Season with salt and pepper. Melt butter in a small saucepan. Add paprika and cayenne; remove from heat. Cover to keep warm.

2. Fill a large, shallow saucepan with 2 inches water; bring to a boil, then reduce heat to a simmer. Break 1 egg into a coffee cup and slowly slide into water. Repeat with remaining egg. Cook until whites are set but yolks are still soft, about 3 minutes. Using a slotted spoon, transfer eggs to a paper towel-lined plate.

3. Divide yogurt mixture between plates. Top with eggs; drizzle with butter mixture. Sprinkle with pepper and chive blossoms; serve.