Preheat the oven to 375°F. Place one unbaked 9-inch pie crust into a pie pan and set aside while you prepare the filling.

Heat a large skillet over medium-high. Add the sliced ribeye and cook, stirring, until mostly browned, about 3–4 minutes. Transfer the beef to a plate and reserve the skillet.

Lower the heat to medium and melt the butter in the same skillet. Add the chopped green pepper, yellow onion, and mushrooms and sauté until the onions are translucent and the vegetables have softened, about 4–5 minutes.

Sprinkle the flour over the vegetables and stir or whisk continuously for about 1 minute to cook the raw flour taste. Season with kosher salt and coarse ground black pepper.

Slowly add the milk and beef broth while whisking to keep the mixture smooth. Stir in the Velveeta or Cheez Whiz and continue cooking, stirring occasionally, until the sauce is thick and creamy, about 6–8 minutes.

Return the cooked ribeye to the skillet and mix thoroughly so the meat is coated in the cheesy gravy and heated through.

Pour the beef and vegetable filling into the prepared bottom crust. Cover with the second crust, trim any excess, and crimp the edges to seal. Cut a few small vents in the top crust to allow steam to escape.

Whisk the egg with the water to make an egg wash, brush it over the top crust, and bake the pie for about 45 minutes, until the crust is golden and the filling is bubbly. Let the pie rest 10–15 minutes before slicing and serving.