In a mixing bowl, combine Greek yogurt with minced garlic, chopped dill, and fresh mint leaves. Season generously with salt and pepper, stirring until well combined. Set aside.

Bring a pot of water to a gentle simmer and add vinegar. Create a whirlpool with a spoon and gently crack in an egg, poaching for 2-3 minutes. Remove with a slotted spoon. Repeat with the second egg.

In a saucepan, melt butter over medium heat. Cook until bubbling; add chili flakes and smoked paprika, cooking for 1-2 minutes to infuse flavors.

On a serving plate, spread a thick layer of herbed yogurt. Place poached eggs on top to create a beautiful presentation.

Drizzle the spiced butter over the eggs and yogurt, garnish with herbs and black pepper, and serve.