Pat the beef dry and season all over with the pepper. Heat the oil in a Dutch oven over medium-high until shimmering. Sear the beef in two batches, undisturbed 3–4 minutes per side, until a dark crust forms. Transfer to a plate.
Add the onion, celery, and carrot to the same pot. Cook 5–6 minutes, scraping up the browned bits, until the onion is translucent. Add the garlic and cook 30 seconds.
Push the vegetables aside, add the tomato paste to the bare spot, and fry 1 minute until it darkens to brick red. Stir through.
Sprinkle over the flour and stir constantly 1–2 minutes. Whisk the gravy mix into the beef broth, then pour in slowly while stirring. Add the Worcestershire, soy sauce, and sugar. Return the beef and its juices.
Bring to a bare simmer, cover, and cook on low 1½ to 2 hours, stirring every 30 minutes, until the beef shreds with no resistance. Stir in the peas and cook 2 minutes more.
Spread the filling in a shallow dish and cool to room temperature, or refrigerate 30 minutes. Do not skip this — warm filling melts the butter in the pastry and kills the flake.
Divide the filling among 4 ramekins, leaving ½ inch of headroom. Cut crust rounds 1 inch wider than each rim, lay over the top, press down the overhang, and crimp. Brush with beaten egg and cut 2–3 steam slits in each.
Preheat the air fryer to 350°F for 3 minutes. Cook the pies at 350°F for 12–15 minutes, until deep golden and bubbling through the slits. Check at 10 minutes; tent with foil if browning too fast. Rest 5 minutes before serving.