Preheat oven to 350 degrees. Spray an 8x12 baking dish with non stick spray.
In a skillet on medium high, cook ground beef, diced onion, and half the salt and pepper until the beef is browned. Stir in the Worcestershire sauce and flour. Cook and stir for 3 minutes until the flour is distributed and browned.
Slowly stir in the water or beef broth. Reduce heat to a simmer and cook until thick, about 5 minutes. Remove from heat.
While beef is cooking, place peeled and cubed potatoes in a large pot of cold water. Heat to high and boil until potatoes are tender and easily pierced with a fork. Drain COMPLETELY. Return potatoes to the pot. Add butter and remaining salt and pepper. Mash with a large fork or potato masher to desired consistency.
Add milk and continue to mash until potatoes are smooth. Adjust amount of milk as needed.
Spread the beef and gravy mixture into the bottom of the prepared baking dish.
Top evenly with the bag of peas and carrots. Then spread the mashed potatoes evenly over the top.
Sprinkle with the shredded cheese and french fried onions.
Bake in oven for 40 minutes until heated through and the cheese is melted and golden.