In a bowl, toss the beef with the flour and season with salt and pepper.
Heat the oil in a large ovenproof skillet over a medium-high heat. Add the beef and cook for 2 minutes until it is browned. Add the onion, garlic, thyme and bay leaves and cook for 5 minutes until the onion is softened.
Add the stock and ale and bring to a boil. Cover with a lid and transfer to the oven to bake for 1 hour.
Remove the skillet from the oven and add the peas and mushrooms. Cover with the puff pastry and brush with the beaten egg. Return to the oven and bake for an additional 30 minutes until the pastry is golden brown.
Steak and Ale Pie is a classic British comfort food.
The pie is traditionally served with mashed potatoes.
The filling can be made ahead of time and frozen for up to three months.