Preheat the oven 300°F. Spray a 2-quart dish (about 8- or 9-inch square baking dish) with cooking spray and set aside.
Melt the butter in a large skillet over medium-high heat. Add the onion and cook for about 5 minutes, until soft and translucent. Add the garlic and cook for 1 more minute.
Add the ground beef, rosemary, thyme, salt and pepper; cook over medium heat until meat is no longer pink. Drain off fat. Stir in tomato paste, beef broth, carrots and peas. Cook and stir over low heat, just until everything is combined.
Transfer meat mixture to prepared baking dish. Spread the mashed potatoes on top.
Cover the dish with a piece of foil that has been sprayed with cooking spray. Bake, covered, for 25 minutes, or until the filling is hot. Increase the oven temperature to 425°F, remove the foil, and return the dish to the oven for about 10 more minutes (or until the potatoes start to brown).
Let the pie rest for 10-15 minutes before garnishing with parsley and serving.