Peel and quarter potatoes, place 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).
Sauté vegetables: While the potatoes are cooking, melt 4 tablespoons of the butter in a large sauté pan on medium heat. Add the chopped onions and carrots cook until tender, about 6 to 10 minutes.
Add ground beef to the pan with the onions and vegetables. Cook until no longer pink. Season with salt and pepper.
Add the Worcestershire sauce and beef broth. Add peas and corn 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.
Mash the cooked potatoes: 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 Tbsp of butter. Mash with a fork or potato masher, and season with salt and pepper to taste.
Layer the meat mixture and mashed potatoes in a casserole dish: Preheat oven to 400°F. Spread the beef, onions, and vegetables in an even layer in a large baking dish (9×13 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.
Bake in oven: 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.