Cut the chuck steak into 1-inch cubes and season it with salt and pepper.
Lightly toss the beef in flour to coat.
Heat olive oil in a large pan over medium-high heat.
Brown the beef cubes in batches to avoid overcrowding.
In the same pan, add more oil if needed.
Sauté the onion, carrots, celery, and garlic until they soften.
Stir in tomato purée and cook for a minute.
Pour in the Guinness, beef stock, and thyme, bringing everything to a boil.
Simmer until the beef is tender and sauce thickens.
Preheat the oven to 400°F (200°C).
Transfer the filling to a pie dish and cover it with the puff pastry, crimping the edges.
Brush with beaten egg and make a small slit in the top.
Bake until the pastry is golden brown.