01 - Preheat your oven to 400°F (200°C).
02 - Place the peeled and cubed sweet potatoes in a large pot. Cover them with cold water, add a pinch of salt, and bring to a boil. Reduce heat and simmer for 15 to 20 minutes, or until they are very tender.
03 - Drain the cooked sweet potatoes thoroughly. Mash them with the butter and milk until smooth and creamy. Season with salt and freshly ground black pepper to taste, then set aside.
04 - While the sweet potatoes are cooking, heat the olive oil in a large skillet over medium heat. Add the finely chopped onion, minced garlic, diced carrots, and diced celery. Sauté for 5 to 7 minutes until the vegetables have softened.
05 - Add the ground beef to the skillet. Cook, breaking it up with a spoon, until it is thoroughly browned and cooked through, approximately 8 to 10 minutes. Drain any excess fat if necessary.
06 - Stir in the tomato paste, dried thyme, dried rosemary, and smoked paprika. Season the mixture with salt and pepper. Continue to cook for 2 minutes to allow the flavors to meld.
07 - Incorporate the frozen peas, beef broth, and Worcestershire sauce into the beef mixture. Bring to a simmer and cook for 5 to 7 minutes, allowing the sauce to thicken slightly.
08 - Transfer the prepared beef filling to a large baking dish. Evenly spread the reserved sweet potato mash over the top of the beef mixture, covering it completely.
09 - Gently use a fork to create decorative ridges on the surface of the sweet potato mash. This will help achieve a golden and crispy texture during baking.
10 - Bake the shepherd's pie in the preheated oven for 20 to 25 minutes, or until the sweet potato topping is golden brown and the filling is bubbling around the edges.
11 - Allow the shepherd's pie to cool for 5 minutes before serving to let it set.