Heat olive oil in a large skillet over medium heat. Add the cubed beef and cook until browned on all sides. Remove the beef from the skillet and set it aside.

In the same skillet, add the diced onion, carrots, and celery. Sauté until the vegetables are tender, about 5 minutes. Add the minced garlic and cook for another minute.

Sprinkle the flour over the vegetables and stir to coat. Slowly pour in the beef broth, stirring constantly to avoid lumps. Bring the mixture to a simmer and cook until the gravy thickens, about 5 minutes.

Return the beef to the skillet and add the frozen peas, thyme, rosemary, salt, and pepper. Stir well to combine and let the mixture simmer for another 5 minutes.

Preheat your oven to 375°F (190°C). Roll out one pie crust and place it in the bottom of a 9-inch pie dish. Pour the beef and vegetable mixture into the crust.

Roll out the second pie crust and place it over the filling. Crimp the edges to seal the pie and cut a few slits in the top crust to allow steam to escape. Brush the top crust with the beaten egg for a golden finish.

Bake the pot pie in the preheated oven for 30-35 minutes, or until the crust is golden brown and the filling is bubbly. Let it cool for a few minutes before serving.