Preheat oven to 375°F.
Melt butter in an extra large skillet over medium heat.
Add diced onion and cook until onions soften and turn translucent.
Sprinkle flour over the onions in the pan and stir cooking the mixture until flour begins to brown lightly.
Stir in the chicken broth and stir until smooth and combined with the flour/onions.
Add cream of chicken soup and whisk to combine. Whisk until mixture is smooth.
Add drained sliced mushrooms. Stir to combine.
Add peas and carrots. Stir to combine.
Add diced chicken and stir to combine.
Taste and season with salt and pepper.
Remove from heat and transfer mixture into a deep sided 13x9 inch oven safe casserole dish.
Unroll crescent roll dough onto a flat work surface. Gently pinch seams together.
Lay the dough on top of chicken filling.
Unroll second tube of cresent roll dough and pinch seams together on one half of the dough forming a long narrow rectangle.
Lay this half sheet of dough over the remaining exposed chicken filling in the casserole dish. Tuck the edges of the dough under along the edges as needed to completely cover the filling.
Baste the crust with the beaten egg.
Bake in the oven for 30 minutes until crust is golden brown and the filling is hot and bubbly.
Serve chicken filling over a bed of creamy mashed potatoes and top each serving with a portion of the crust.