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Place the peeled and quartered potatoes in medium sized pot. Cover with at least an inch of cold water. Add a teaspoon of salt. Bring to a boil, reduce to a simmer, and cook until tender (about 20 minutes). Preheat the oven to 400°F.
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While the potatoes are cooking, melt 4 tablespoons of the butter in a large sauté pan on medium heat. Add the chopped onions and cook until tender, about 6 to 10 minutes. Then cook all your veggies.
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Add ground mutton to the pan with the onions and vegetables. Cook until no longer pink. Drain the pan of excess fat, if necessary (anything more than 1 tablespoon). Season with salt and pepper.
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Add the Worcestershire sauce and beef broth. Bring the broth to a simmer and reduce heat to low. Cook uncovered for 10 minutes, adding more beef broth if necessary to keep the meat from drying out.
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When the potatoes are done cooking (a fork can easily pierce), remove them from the pot and place them in a bowl with the remaining 4 tablespoons of butter. Mash with a fork or potato masher, taste, and adjust seasonings with salt and pepper.
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Spread the cooked filling in an even layer in a large baking dish (such as a 9 x 13-inch casserole. Spread the mashed potatoes over the top of the ground beef. Rough up the surface of the mashed potatoes with a fork so there are peaks that will get well browned. You can even use a fork to make creative designs in the mashed potatoes.
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Place in a 400°F oven and cook until browned and bubbling, about 30 minutes. If necessary, broil for the last few minutes to help the surface of the mashed potatoes brown.