Preheat the oven to 375°F (190°C).
In a large pan over medium heat, cook the ground beef until browned. Drain any excess fat.
Add the onion and garlic to the pan and sauté until the onion is translucent.
Stir in the flour and cook for 1-2 minutes.
Gradually add the beef broth, stirring constantly, and bring to a simmer. Cook until the mixture thickens, about 5 minutes.
In a pot, boil the potatoes until tender. Drain and mash with butter, salt, and pepper.
Roll out the pie crust and fit it into a pie dish. Pre-bake for 10 minutes.
Fill the pie crust with the beef mixture, then layer the mashed potatoes on top.
Bake in the preheated oven for about 25-30 minutes, until the top is golden brown.
Let the pie cool for a few minutes before serving.