Fill a large pan with water and bring to boil. Add the potatoes and cook until easily pierced with a fork.
Meanwhile, take one layer of rolled pie dough and place on the bottom of the pie pan. Bake according to the pie dough directions. Remove from the oven and set aside.
While the crust bakes, melt the butter in a large skillet over medium heat. Add the onions and cook until tender, about 5-8 minutes. Whisk the flour into the butter and onions. Cook until golden, about 8-10 minutes. Continue to whisk frequently to prevent burning.
Place the chicken stock and cream into a bowl and heat in the microwave for 3 minutes. Slowly whisk in the chicken stock mixture and flank steak pan sauce into the skillet until well combined. Add the thyme bundle to the sauce. Bring the sauce to a simmer. Cook for 15 minutes, or until the sauce is thickened. Stir frequently.
Meanwhile, turn the oven on to 450 degrees.
Add the peas, mushrooms and steak into the sauce. Stir well and let warm through, about 5 minutes. Pour the mixture into the baked shell, then cover with the remaining piece of dough. Make a small X in the center of the pie dough, to allow the pie to vent while cooking.
Brush the top of the pie dough with egg wash. Place in the oven and bake for 15 minutes, or until the dough is golden brown. Serve warm with mashed potatoes (see notes for recipe).