In a mixing bowl, combine yogurt with minced garlic, chopped fresh dill, and fresh mint leaves. Season with salt and pepper to taste. Set aside at room temperature.

Fill a deep pot with water and bring it to a gentle boil over medium-high heat. Add vinegar, create a whirlpool, and carefully drop in the eggs. Cook for 2-3 minutes until the whites are set.

In a small skillet, melt butter over medium heat. Stir in chili flakes and smoked paprika. Cook for 1-2 minutes until fragrant, then remove from heat.

On a serving plate, spread the herbed yogurt base, place the poached eggs on top, and drizzle with spiced butter. Garnish with herbs and a sprinkle of black pepper.