Finely chop the fresh dill and mint leaves, then combine them in a bowl with the yogurt, crushed garlic, salt, and pepper. Stir well until all the ingredients are evenly blended, creating a creamy and fragrant base. Set aside at room temperature.

In a deep pot, bring about 3 inches of water to a gentle boil over medium heat. Add the vinegar, then create a gentle swirl. Crack one egg into a small cup and carefully drop it into the center of the vortex. Cook for 2-3 minutes until the whites are set, then remove with a slotted spoon and repeat with the second egg.

In a small saucepan over low heat, melt the butter until it starts to foam. Add the chili flakes and smoked paprika, stirring well. Cook for about 2 minutes until the spices warm through without burning.

On a serving plate, spread a layer of the herbed yogurt mixture, place the poached eggs on top, drizzle with spiced butter, and sprinkle with extra herbs for presentation.