Combine beef broth, Worcestershire sauce, tomato paste, and Dijon mustard; whisk until well blended. Set aside.
Brown ground beef in a large non-stick skillet. Drain in a colander and rinse well with hot water to remove as much fat as possible. Wipe the skillet with a paper towel and place over medium heat. (See Tip 3)
Heat olive oil or butter in a skillet over medium heat. Add onion and carrots; cook until tender, about 5 minutes. Add ground beef, flour, salt, and pepper. Stir to combine. Cook for several minutes. Add beef broth mixture; cook, constantly stirring over medium heat, until bubbly and thickened. Cover and continue cooking over medium-low heat for 45 minutes or until the meat and vegetables are tender. (See Tip 4)
Add the frozen peas and stir to combine all ingredients. (See Tip 5)
Spoon into a buttered casserole dish(es). Pipe mashed potatoes over the meat mixture. May be prepared in advance up to this point. (See Tip 6)
Bake at 375º F for 25 to 30 minutes, or until the top of the potatoes is lightly browned, and the mixture is bubbly. Yield: 8 servings. (See Tip 7)