Place the cubed potatoes in a large pot of cold, salted water. Bring to a boil and simmer 15–18 minutes, until a chunk breaks easily with a fork. Drain and let steam dry for 1 minute.
Transfer potatoes to a large bowl. Add 4 tablespoons of the butter, the sea salt, and the warm milk. Mash until smooth and creamy. Set aside.
While the potatoes cook, crumble the ground beef into a casserole dish that fits your air fryer basket with at least 1 inch of clearance. Stir in the diced onion. Air fry at 400°F for 10 minutes, stirring at the halfway point.
Stir the beef again, breaking up any clumps. Add the minced garlic, herbs, black pepper, 1/2 teaspoon salt, Worcestershire sauce, flour, tomato paste, and beef broth. Stir until fully combined.
Fold in the peas, carrots, and corn. Press the filling down into an even, level layer.
Mound the mashed potatoes over the filling and spread to the edges, sealing them to the sides of the pan. Drag the back of a spoon through the surface to create peaks and valleys.
Cut the remaining 4 tablespoons of butter into small pieces and scatter across the top.
Return the dish to the air fryer and cook at 380°F for 8–10 minutes, until the butter has melted and the potato peaks are golden brown.
Remove carefully, garnish with fresh parsley, and rest 5 minutes before slicing.