Preheat your oven to 400°F (200°C). Lightly grease a 9x9 inch baking dish.
In a large skillet over medium-high heat, brown the ground beef along with the chopped onion and diced carrots until the meat is cooked through and vegetables are tender. Drain any excess fat.
Stir in the tomato paste, Worcestershire sauce, beef broth, and frozen peas. Bring the mixture to a simmer and cook for 5 minutes until the gravy has slightly thickened. Season with salt and pepper to taste.
Transfer the savory beef mixture into the prepared baking dish, spreading it into an even layer.
Spoon the warm mashed potatoes over the beef filling. Spread gently to the edges to create a seal, then rough up the surface with a fork to create peaks that will crisp in the oven.
Bake uncovered for 20 to 25 minutes, or until the potato topping is golden brown and the filling is bubbly around the edges.
Remove from the oven, garnish with fresh parsley, and let rest for 10 minutes before serving.