Preheat oven to 375F.
In a large skillet set over medium-high heat, cook the ground beef and onion until the onion is soft and the beef is no longer pink. Sprinkle the flour overtop and stir to distribute it, then pour in the beef stock, add the tomato paste and Worcestershire, and stir to blend well. Bring to a simmer and cook for a minute or two, until the gravy thickens. Add the carrots and peas, season with salt and pepper and pour into a baking dish that will accommodate it.
Meanwhile, pour cold water over the potatoes in a medium-large pot and bring to a boil. When they're very tender, drain and mash them (rough or smooth) with the butter and milk and spread over the beef mixture. Scatter the grated cheese overtop. Bake for 30 minutes, or until the top is golden and it's bubbly around the edges.