Prepare the Avocado: Slice the avocado lengthwise around the pit. Twist the halves apart, carefully remove the pit, and peel away the skin while keeping both halves intact.
Trim the Avocado: Cut a thin slice from the rounded bottom of one avocado half to create a flat, stable base. Place it on a cutting board with the hollow side facing up.
Season the Avocado: Sprinkle the hollow center of the bottom avocado half with ⅛ teaspoon salt and ⅛ teaspoon ground black pepper.
Spread the Greek Yogurt: Spoon 1 teaspoon of plain Greek yogurt into the center of the seasoned avocado half. Gently spread it into a thin, even layer.
Add the Lettuce: Fold the romaine lettuce leaf to fit over the avocado half. Place it on top of the yogurt, pressing gently so it stays in place.
Layer the Smoked Salmon: Arrange 1 ounce of smoked salmon over the lettuce. Fold the salmon into a compact layer so it fits neatly inside the avocado burger.
Fry the Egg: Heat 1 teaspoon of cooking oil in a nonstick skillet over medium heat. Crack the egg into the skillet and cook sunny-side up for approximately 3–4 minutes, or until the white is completely set and the yolk remains soft and runny. Do not flip the egg.
Add the Fried Egg: Carefully lift the cooked egg from the skillet using a spatula. Place it over the smoked salmon, keeping the yolk intact. Position the egg so it sits evenly on the burger.
Complete the Avocado Burger: Gently place the remaining avocado half over the fried egg, rounded side facing up. Adjust the layers carefully to keep the burger balanced.
Garnish with Sesame Seeds: Sprinkle ¼ teaspoon of black sesame seeds evenly over the top avocado half.
Serve Immediately: Transfer the assembled avocado burger to a serving plate and enjoy while the egg is warm and the avocado is fresh and creamy.