01 - Preheat oven to 400°F.
02 - Place sweet potatoes in a large pot of salted water. Bring to a boil and cook for 15 to 20 minutes until very tender. Drain thoroughly.
03 - Mash the sweet potatoes with butter, milk, salt, and pepper until smooth. Set aside.
04 - Heat olive oil in a large skillet over medium heat. Add chopped onion and diced carrots; sauté for 4 to 5 minutes until softened.
05 - Add minced garlic and cook for 1 minute. Incorporate ground beef and cook until browned, breaking up the meat with a spoon.
06 - Stir in tomato paste, Worcestershire sauce, thyme, rosemary, salt, and pepper. Cook for 1 minute. Pour in beef broth, add peas, and simmer for 5 to 7 minutes until the sauce thickens slightly.
07 - Spread the beef mixture evenly in an 8 x 8 inch baking dish.
08 - Spoon the sweet potato mash over the beef layer, smoothing the surface with a spatula.
09 - Bake for 20 minutes until the top is lightly golden and the filling is bubbling.
10 - Allow to cool for 5 minutes before serving.