Preheat the air fryer to 400°F for 3 minutes while you prep a single shallow layer.
Pat salmon cubes completely dry with paper towels, then place in a medium bowl and sprinkle with cornstarch, tossing until evenly coated.
Add lemon pepper seasoning, kosher salt, and olive oil to the bowl and toss gently to coat; pieces should glisten but not be dripping.
Arrange salmon in a single layer in the air fryer basket, leaving space between pieces; cook at 400°F for 8 minutes, then check doneness.
If needed, continue cooking 1–2 minutes until an instant-read thermometer reads 125–130°F and pieces flake easily at the thickest part.
Transfer to a bowl, toss with melted butter, lemon juice, and lemon zest, garnish with chopped parsley, and serve immediately.