In a large pot, bring the chicken stock to a boil. Add the carrots, celery and simmer for about 15 minutes, or until veggies are almost tender. Add the frozen peas and continue to simmer a minute or two more. Remove veggies to a large bowl with a slotted spoon and reserve stock. Add chopped chicken or turkey to the veggies and set aside.
Now, preheat the oven to 450.
In a dutch oven, melt the butter. Add the onions and the mushrooms and saute for about seven minutes, or until both onions and mushrooms are soft. Now, slowly pour in the remaining stock, whisking as you pour. Add cream of chicken soup to the liquid and whisk until smooth and heated through, for about five minutes. Add the Italian seasoning, salt and pepper and stir. Pour the sauce over the chicken (or turkey) and veggies and stir until well combined. Pour and spread evenly into a greased 9x13 inch casserole dish.
Place biscuit rounds on top of the filling and brush the tops of the biscuits with egg wash (just one yolk mixed with a little warm water—this gives the biscuits shine) and prick with a fork.
Bake for about 20 minutes, or until the biscuits are golden and the chicken mixture is bubbling. Serve hot.