01 - Set oven temperature to 400°F (200°C).
02 - Place cubed sweet potatoes in a large pot, cover with cold water, add a pinch of salt, bring to a boil, then simmer for 15-20 minutes until tender.
03 - Drain potatoes thoroughly, then mash with butter, milk, salt, and pepper until smooth. Set aside.
04 - Heat olive oil in a large skillet over medium heat. Add onion and cook until softened, about 2-3 minutes.
05 - Incorporate garlic and diced carrots into the skillet and cook for an additional 3 minutes.
06 - Add ground beef, breaking it up with a wooden spoon, and cook until browned, approximately 5-7 minutes.
07 - Stir in tomato paste, Worcestershire sauce, thyme, and rosemary; cook for 2 minutes to combine flavors.
08 - Pour beef broth into the skillet, bring to a simmer, and cook for 5 minutes until the mixture thickens slightly.
09 - Fold in frozen peas and season well with salt and freshly ground black pepper. Remove from heat.
10 - Transfer beef filling into a 2-quart baking dish and spread the sweet potato mash evenly over the top.
11 - Use a fork to create ridges across the mashed sweet potatoes to enhance crispness during baking.
12 - Bake in the preheated oven for 20-25 minutes until the topping is golden and the filling bubbles.
13 - Allow to rest for 5 minutes before serving to set the layers.