Place the peeled and chopped potatoes in a large pot of salted water, bring to a boil, and cook for 15 minutes or until tender. Drain well and mash with the butter and milk until smooth and creamy, seasoning with salt and pepper to taste.

While the potatoes cook, heat a large skillet over medium-high heat and add the ground lamb. Cook for 5-7 minutes, breaking it apart with a spoon, until browned and cooked through.

Add the diced onion and carrots to the skillet with the lamb. Sauté for another 5 minutes until the vegetables soften and the onions become translucent.

Stir in the minced garlic, tomato paste, rosemary, and flour. Cook for 1-2 minutes, stirring constantly to coat the meat and vegetables and remove the raw flour taste.

Pour in the beef broth and Worcestershire sauce, scraping up any browned bits from the bottom of the pan. Bring to a simmer and let it thicken for about 3-4 minutes, then stir in the frozen peas.

Preheat your oven to 400°F (200°C). Transfer the lamb mixture into a 9x9 inch baking dish or casserole dish, spreading it out into an even layer.

Spoon the mashed potatoes over the meat filling. Use a fork to spread the potatoes to the edges and create a rough texture on top, which will help them brown nicely.

Bake in the preheated oven for 20-25 minutes. The shepherd's pie is done when the filling is bubbling around the edges and the potato topping is golden brown.

Remove from the oven and let it rest for 10 minutes before serving. This allows the filling to set slightly, making it easier to serve clean slices.