How to make steak and ale pie

Name: How to make steak and ale pie
Prep time: 2 h
Cook time: 2 h
Total time: 4 h
Cuisine: British
Ingredients: 225g/8oz plain flour, plus extra for rolling out; ½ tsp fine salt; 250g/9oz unsalted butter, cold but not rock hard (or you can use half butter, half lard); 150ml/¼ pint ice-cold water; 1 free-range egg, beaten, to glaze; 1 kg/2lb 4oz braising steak, cut into matchbox-sized pieces; 3 tbsp plain flour; 3 tbsp olive oil; 300ml/½ pint brown ale; 2 garlic cloves, roughly chopped; 2 onions, roughly chopped; 250g/9oz carrots, roughly chopped; 2 sticks celery, roughly chopped; 1 bay leaf; handful fresh thyme sprigs; 300ml/½ pint good-quality beef stock; 1 tbsp tomato purée; 1 tbsp balsamic vinegar; 500g/1lb 2oz chestnut or white mushrooms, halved or cut into quarters if large; knob of butter; salt and freshly ground black pepper