01 - Preheat the oven to 400°F (200°C).
02 - Place sweet potatoes in a large pot of salted water and bring to a boil. Cook until very tender, about 15 to 20 minutes. Drain thoroughly.
03 - Mash sweet potatoes with butter, milk, salt, and black pepper until smooth. Set aside.
04 - Heat olive oil in a large skillet over medium heat. Add onion and carrots; sauté until softened, about 4 to 5 minutes.
05 - Add garlic to the skillet and cook for 1 minute. Add ground beef and cook until browned, breaking up meat with a spoon.
06 - Stir in tomato paste, Worcestershire sauce, dried thyme, dried rosemary, salt, and black pepper. Cook for 1 minute to combine flavors.
07 - Pour in beef broth, add frozen peas, and simmer for 5 to 7 minutes until the sauce thickens slightly.
08 - Spread the beef mixture evenly in an 8 x 8 inch (20 x 20 cm) baking dish.
09 - Spoon the sweet potato mash over the beef filling and smooth the surface with a spatula.
10 - Bake for 20 minutes, or until the top is lightly golden and the filling is bubbling.
11 - Allow the dish to rest for 5 minutes before serving.