01 - Preheat the oven to 400°F (200°C).
02 - Place sweet potatoes in a large pot, cover with cold water, add a pinch of salt, and bring to a boil. Simmer for 15 to 20 minutes until very tender.
03 - Drain the cooked sweet potatoes. Mash them with butter and milk. Season with salt and pepper to taste, then set aside.
04 - While sweet potatoes cook, heat olive oil in a large skillet over medium heat. Add onion, garlic, carrots, and celery; cook for 5 to 7 minutes until softened.
05 - Add ground beef to the skillet; cook, breaking it up, until browned and cooked through, about 8 to 10 minutes.
06 - Stir in tomato paste, dried thyme, dried rosemary, and smoked paprika. Season with salt and pepper. Cook for an additional 2 minutes.
07 - Add frozen peas, beef broth, and Worcestershire sauce. Simmer for 5 to 7 minutes until the sauce slightly thickens.
08 - Transfer the beef mixture to a large baking dish.
09 - Evenly spread the sweet potato mash over the beef filling.
10 - Use a fork to create decorative ridges on the mash for a crispy finish.
11 - Bake for 20 to 25 minutes, or until the topping is golden and the filling is bubbling.
12 - Allow the pie to cool for 5 minutes before serving.