01 - Preheat the oven to 400°F (200°C).
02 - Place sweet potatoes into a large pot of salted water. Bring to a boil and simmer for 15 to 18 minutes until tender. Drain thoroughly.
03 - Add butter and milk to the drained sweet potatoes. Mash until smooth and season with salt and pepper. Set aside.
04 - Heat olive oil in a large skillet over medium heat. Add onion, carrots, and celery. Cook for 5 to 6 minutes until softened.
05 - Add minced garlic and cook for 1 minute. Incorporate ground beef, breaking it up with a spoon, and cook for 6 to 8 minutes until browned. Drain excess fat if necessary.
06 - Stir in tomato paste, thyme, rosemary, and Worcestershire sauce. Cook for an additional 2 minutes.
07 - Pour in beef broth, bring to a simmer, and cook for 10 minutes, stirring occasionally. Add frozen peas during the last 2 minutes. Season with salt and pepper.
08 - Transfer the beef mixture into a 2-quart baking dish. Spread the sweet potato mash evenly over the top.
09 - Use a fork to texture the mash surface. Bake in the preheated oven for 20 to 25 minutes until the filling bubbles and the mash turns lightly golden.
10 - Remove from oven and allow to rest for 5 minutes prior to serving.