Take a large, heavy-bottomed pan. Heat the vegetable oil in it. Brown the steak pieces on all sides and set aside.
In the same pan put the onions and carrots. Sauté them until they start to soften.
Return the steak to the pan with the vegetables. Sprinkle over the flour and stir, cooking for a minute.
Add the thyme, red wine, and beef stock. Bring to a simmer. Now cover and cook gently for about 1.5 hours. Meanwhile, the steak will become tender.
Preheat your oven to 200°C (390°F).
Stir in the whole mushrooms and cook for a further 10 minutes. Remove from heat and let the mixture cool slightly.
Roll out the puff pastry. Pour the steak and mushroom mixture into a large pie dish.
Cover with the puff pastry, trimming and crimping the edges. Make a few slits on top for steam to escape.
Bake for 25-30 minutes, or until the pastry is puffed and golden brown.