Heat ¾ tablespoon butter in nonstick pan over low heat. Melt the butter slowly; the butter should not foam or sizzle. Carefully crack the eggs into the pan, one by one. Cover the pan with a lid and cook for 5 minutes or until the whites have solidified and the yolks have slightly thickened.
Meanwhile, toast bread until golden brown. In a small bowl, combine the avocado with the lime juice and season with salt and pepper. Spread ½ avocado onto each toast followed by sliced cucumber and 2 oz smoked salmon.
Slide egg onto prepared toasts. Season with salt and pepper and finish toasts with ½ tablespoon pesto per toast. Serve immediately.