This is a modified recipe from old England. It has been updated for quicker preparation and using modern ingredients. I learned it from my grandmother and she from hers.
Prepare mashed potatoes. Set aside.
In large deep skillet add onion and ground ground beef, cook until beef is done and onion just tender. Drain fat. Add 4 cups beef broth. Heat to boiling. While broth mixture is heating mix the dumplings.
In a large mixing bowl add together flour, dash of salt, baking powder, and 3 eggs. Mix together until well mixed and forms ball. If mixture is still dry add the other egg. Turn onto well-floured surface and form into ball as for making noodles. Cut into nickle size balls or smaller.
As soon as broth is boiling, add dumplings and simmer until tender. If broth becomes too thick add more broth as needed to thin slightly.
As soon as dumplings are tender, thicken mixture with flour to a thick gravy. Fold in the peas and carrots.
Transfer mixture to a large 9 x 13 metal or glass baking pan. Sprinkle top of mixture with two-thirds of the cheese. Spread mashed potatoes over top of mixture.
Sprinkle the rest of the cheese and the green onions on top of the potatoes.
Bake in preheated oven at 375 degrees until well heated and potatoes are browned. Cheese and onions will brown first, so once they brown you can remove from oven. Let cool 5 minutes and then serve.