Start by melting the butter in a small non-stick skillet over medium-low heat until it begins to bubble gently and releases a fragrant aroma, about 1-2 minutes.
Add smoked paprika and chili flakes to the melted butter, stirring briefly until fragrant, about 30 seconds. This creates a spicy, smoky butter base.
Reduce heat to low, then create a gentle whirlpool in the skillet with a spoon. Carefully crack each egg into a small bowl first, then slide them gently into the simmering butter near the center of the pan. This helps control placement and shell checks.
Cook the eggs for about 2-3 minutes, until the whites are just opaque and set around the yolk, which should remain soft and runny. Gently jiggle the pan to check for doneness.
Meanwhile, in a small bowl, whisk together the Greek yogurt with lemon juice, a pinch of salt, and freshly ground pepper until smooth and creamy. Taste and adjust seasonings as desired.
Using a slotted spoon, carefully lift the eggs from the butter, letting excess butter drain off, and place a generous spoonful of the yogurt mixture on each plate.
Gently slide the eggs over the yogurt, then spoon the fragrant butter sauce over the top, ensuring the yolks stay soft and inviting.
Finish with a light sprinkle of extra chili flakes or paprika if desired, and serve immediately while warm for the best creamy, runny yolks and aromatic sauce.
