Preheat oven to 375 degrees F.
Allow piecrust to warm at room temperature,15-20 minutes, before rolling out.
Spray a 2-quart casserole dish with non-stick cooking spray.
Heat butter and oil over medium-high heat until it shimmers.
Add diced carrots and celery and cook for 3 minutes.
Add minced onions and cook until onion is translucent.
Add minced garlic and cook 30 seconds.
Add cubed, cooked chicken and diced mushrooms and cook 1 minute.
Sprinkle vegetables and chicken with the flour and cook 3 minutes, stirring continuously.
Stir in chicken stock and scrape the bottom of the pan to deglaze the pan.
Pour in the white wine and cream. Stir well.
Season-to-taste with salt and add the pepper, thyme and basil. Stir well and continue to cook until thickened to a thick-stew consistency.
Pour chicken stew mixture into the prepared casserole dish.
Roll the piecrust to ¼ inch thickness and into 1-inch strips to create a lattice top. Or, drape it over the chicken stew mixture, and trim or crimp in the sides. Combine egg and water and brush the pastry with the egg mixture.
Bake, at 375 degrees F, on the center rack of the oven, 35-45 minutes, or until top is golden.