In a large Dutch oven, heat 2 tablespoons of oil over medium-high heat until shimmering. Add the beef chuck in batches, sear for 4-5 minutes on each side until browned, then transfer to a plate.

In the same pot, add another tablespoon of oil and reduce heat to medium. Stir in mushrooms, carrots, and celery; cook for 5-7 minutes until softened.

Sprinkle 2 tablespoons of flour over the sautéed vegetables, stirring constantly for about 2 minutes until the flour deepens in color. Mix in 2 tablespoons of tomato paste and your favorite herbs and spices. Deglaze by pouring in the Guinness stout, scraping up the brown bits. Let it bubble and thicken for 3-4 minutes.

Return the browned beef to the pot and cover it with the stout mixture. Bring to a gentle simmer, cover, and reduce heat to low. Braise for about 2 hours until fork-tender.

Remove from heat and let the filling cool for at least 30 minutes. Portion into ramekins or a deep pie dish.

Preheat your oven to 400°F (200°C). Roll out the puff pastry or pie crust until 1/8 inch thick. Drape over the cooled filling, trimming excess and crimping the edges. Cut a few slits in the top crust for steam to escape.

Brush the top crust with an egg wash made from one beaten egg. Bake for 25-30 minutes, or until the crust is golden brown and puffed.