In a large cast iron skillet, or shallow dutch oven, melt the butter over medium heat. Once melted add the onion, carrots, and celery and saute until the veggies have just begun to soften.
Sprinkle the flour over the veggies, stirring to combine. Let cook for 60 seconds.
Add the beef broth, barbecue sauce, rub, and beer. Whisk together vigorously until the mixture's smooth.
Bring the filling to a simmer, and let it continue to cook until thickened.
Stir in the peas and beef, then remove from heat and set aside.
Keep your pie crust in it's sealed plastic sleeve, and defrost in the microwave for 10 seconds. Use DEFROST, and not the regular cook time, to make it more pliable.
Carefully unroll the warmed pie crust and place it evenly over the top of your dish. Carefully press any excess into the edges of the dish like a crust and sealing in the filling- it's still piping hot and you don't want to burn yourself.
Using a sharp paring knife, cut three small slits in the center of the cobbler to allow steam to escape as it cooks.
Break the egg into a bowl, and whisk together until beaten. Using a pastry brush, brush the pie crust liberally with the beaten egg.
Bake the cobbler at 400°, just until the crust is cooked through and a crisp golden brown.