Preheat an air fryer to 400°F. Dice potato into breakfast hash-sized bites, toss in a bowl with a drizzle of olive oil, salt and pepper, and air fry until golden and crispy, about 12-15 minutes (shaking half way through.)
Meanwhile, make the dressing: In a food processor or mason jar with lid, add cream cheese, dill, lemon juice and pepper. Pulse or shake vigorously, then add olive oil and pulse or shake again until well combined.
In a large mixing bowl, toss arugula, chives, red onion and cooked potatoes to combine. Drizzle half of the dressing over the salad and toss again. Plate and top with the smoked salmon and an egg, then drizzle remainder of dressing to taste.
Buon appetito!