Place the beef, salt, pepper and flour in a bowl and toss to combine. Heat the oil in a heavy-bottomed pot set over medium-high heat. Shake the excess flour off the beef; reserve the leftover flour. Brown the beef in the hot oil. Add the onion, carrot, celery and garlic and cook 3 to 4 minutes more. Mix in the reserved flour, tomato paste and thyme; slowly stir in the stock. Bring to a gentle simmer. Reduce the heat until the stew maintains a gentle simmer. Loosely cover and cook for 40 to 45 minutes, or until beef is tender.
Meanwhile, place the puff pastry on a lightly floured surface. Roll into a 10" square. Cut the pastry into four, 4" circles. Place the circles on a parchment paper-lined baking sheet; brush with the beaten egg. Chill the pastry circles in the fridge for 10 minutes. Preheat the oven to 375 degrees F. Bake the pastry for 20 minutes, or until puffed and golden.
Stir the peas into the stew and heat through. Spoon the stew into four individual serving dishes. Top each portion with a round of pastry and serve.