Steak and stout pie

Name: Steak and stout pie
Ingredients: 350g/12oz ready-rolled shortcrust pastry, for the base; 350g/12oz ready-rolled puff pastry, for the lid; plain flour, for dusting; 1 free-range egg, beaten, to glaze; 3–4 tbsp vegetable oil, plus more for drizzling if needed; 900g/2lb rump steak, cut into bite-sized chunks; 2 large brown onions, finely chopped; 2 large celery sticks, finely chopped; 6 large garlic cloves, finely chopped; 3 tbsp plain flour; 1 fresh thyme sprig; 2 bay leaves; 300ml/10fl oz chicken stock; 500ml/18fl oz Irish stout (such as Guinness); 150g/5½oz button mushrooms, kept whole; 2 large carrots, cut into chunks; salt and freshly ground black pepper