Place peeled potatoes in a large pot, cover with cold water, and bring to a boil. Cook until fork-tender, about 20 minutes, then drain and set aside.
Meanwhile, heat a skillet over medium heat and add butter. Once melted, sauté chopped onions and minced garlic until fragrant and translucent, about 5 minutes.
Add ground beef to the skillet, breaking it apart with a spoon. Cook until browned and crispy, about 8 minutes, then drain excess fat if needed.
Stir in diced carrots and peas, cooking until vegetables are tender, about 5 minutes. Season with salt, pepper, and Worcestershire sauce for flavor.
Return drained potatoes to the pot. Add butter, milk, and ground nutmeg. Mash until smooth and creamy, adjusting with more milk if needed.
Spread the meat and vegetable mixture evenly in a baking dish, creating a hearty layer.
Spoon the mashed potatoes over the meat layer, smoothing the surface with the back of a spoon or spatula.
Bake in a preheated oven at 200°C (390°F) for 25-30 minutes until the top is golden brown and bubbling around the edges.
Remove from oven and let sit for a few minutes before serving. The top should be crispy and the filling hot and fragrant.