01 - Set the oven temperature to 400°F (200°C).
02 - Place peeled and cubed sweet potatoes in a large pot, cover with cold water and add a pinch of salt. Bring to a boil, then simmer for 15-20 minutes until tender.
03 - Drain sweet potatoes and mash together 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 cook for 2-3 minutes until softened.
05 - Stir in minced garlic and diced carrots, cooking for an additional 3 minutes.
06 - Add lean ground beef to the skillet, breaking it up with a spoon. Cook until browned, about 5-7 minutes.
07 - Mix in tomato paste, Worcestershire sauce, dried thyme, and rosemary. Cook for 2 minutes to combine flavors.
08 - Pour in beef broth, bring the mixture to a simmer, and cook for 5 minutes until slightly thickened.
09 - Stir in frozen peas, then season with salt and freshly ground black pepper to taste. Remove from heat.
10 - Spoon the beef filling into a 2-quart baking dish and spread the sweet potato mash evenly over the top.
11 - Use a fork to make ridges in the mashed sweet potatoes for a crisped surface.
12 - Bake in the preheated oven for 20-25 minutes until the topping is golden and the filling is bubbling.
13 - Allow to rest for 5 minutes before serving to set.