Heat 1 tablespoon of vegetable oil in a large oven-safe pot or Dutch oven over medium-high heat. Season the beef chuck and diced kidneys generously with salt and black pepper, then sear in batches until browned on all sides, about 5 to 7 minutes per batch. Remove the meat and set aside on a plate.

In the same pot, add the remaining tablespoon of oil along with the chopped onion and carrots. Sauté over medium heat until the onions are soft and translucent, scraping up any browned bits from the bottom of the pot, about 5 minutes.

Sprinkle the flour over the softened vegetables and stir constantly for 1 minute to cook off the raw flour taste. Stir in the tomato paste and fresh thyme, cooking for another 30 seconds until deeply fragrant.

Pour in the brown ale and beef broth, stirring well to combine and ensuring no lumps remain. Return the browned beef, kidneys, and any resting juices to the pot, bringing the liquid to a gentle simmer.

Cover the pot, reduce the heat to low, and simmer gently for 1 hour and 30 minutes, or until the beef is very tender and the gravy has thickened perfectly. Remove from heat and let it cool slightly while you preheat the oven to 400 degrees F.

Transfer the meat filling to a 9-inch deep pie dish. Unroll the thawed puff pastry sheet and drape it over the top of the dish, trimming any excess and crimping the edges to seal the pie.

Brush the top of the pastry evenly with the beaten egg and cut a small slit in the center to allow steam to escape. Bake for 25 to 30 minutes until the pastry is puffed and deeply golden brown, then let the pie rest for 10 minutes before serving with a side of mashed potatoes.