Preheat the oven to 375. In a large skillet, combine the beef, carrots, onion, celery, garlic, & potato – cook over medium-high, breaking up the meat, until the beef is cooked through. Drain the grease if desired (I desire).
Add the beer into the mixture, & cook over medium heat for 15 minutes. Turn off the heat, & add the cheese, salt, & pepper.
On a lightly floured surface, roll 1 puff pastry into a 12 inch round. Place in a deep dish pie plate or oven safe skillet. Roll the remaining puff pastry sheet into an 11 inch round. Using a slotted spoon, transfer the meat & veggie mixture into the pie dish. Lightly brush the edge of the crust with the egg wash, then place the second sheet on top. Press the edges to seal, trimming if need be.
Place the pie on a baking sheet, & brush with the remaining egg wash. Cut an X into the top…you know, to mark the treasure while letting the steam escape.
Bake for 15 minutes. Place a tinfoil ‘tent’ on top to keep the crust from getting to dark, & bake for an additional 30 minutes. Transfer to a wire rack & let cool for 10 minutes before slicing.