Step 1: Make the Sweet Potato Mash : Place cubed sweet potatoes in a large pot of salted water. Bring to a boil and cook until tender, about 15 minutes. Drain well and return to the pot. Add butter and milk, then mash until smooth and creamy. Season with salt, pepper, and optional nutmeg. Set aside.
Step 2: Prepare the Beef Filling : Preheat the oven to 375°F (190°C). Heat olive oil in a large skillet over medium-high heat. Add ground beef and cook until browned, breaking it apart with a spoon. Drain excess fat if necessary. Add onion, garlic, and carrot; sauté until softened, about 5 minutes. Stir in tomato paste, thyme, rosemary, salt, and pepper. Cook for 1 minute to develop flavor. Sprinkle flour over the mixture and stir well. Pour in beef broth and Worcestershire sauce. Bring to a simmer and cook for 5–7 minutes, until thickened. Stir in peas (or mixed vegetables). Taste and adjust seasoning as needed.
Step 3: Assemble the Shepherd’s Pie : Spread the beef mixture evenly in the bottom of a greased 9x13-inch (or similar) baking dish. Spoon the mashed sweet potatoes over the beef, smoothing with a spatula to cover completely. Use a fork to create texture on top (optional, helps browning).
Step 4: Bake : Bake uncovered for 25–30 minutes, or until the top is slightly golden and the filling is bubbling around the edges. For a more golden top, broil for 2–3 minutes at the end (watch carefully).