Preheat your oven to 350ºF. In a large gallon-size Ziploc bag combine the beef, flour and salt, and pepper. Shake to coat. Meanwhile, heat a large Dutch oven over medium heat with half of the oil. Add half of the beef and cook until browned on all sides. Remove to plate and repeat with remaining oil and beef.
To the pan add the onion, celery, carrots and garlic. Add in the water and cook until tender, stirring the bottom of the pan to pick up browned bits. Once tender add in the tomato paste and cook 1 minute.
Add the beef back into the Dutch oven and add the broth, beer, Worcestershire, thyme and season with salt and pepper. Cover and place in the oven, cooking until tender, about 1 hour.
Once tender, remove from the oven and prepare the crust. Preheat oven to 425ºF. Unfold the puff pastry and cut into 6 equal sqaures. Place on a large baking sheet. Whisk together the egg and 1 Tsp water and brush on puff pastry. Bake until golden brown, about 15 minutes. Serve