Preheat the oven to 375 degrees F (190 degrees C).
Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 10 minutes. Drain.
Mash potatoes and add 1/2 cup Cheddar cheese, milk, green onion, and butter. Stir until mixed well.
Heat a large skillet over medium-high heat. Cook and stir ground beef in the hot skillet with flour and pepper until browned and crumbly, 5 to 7 minutes. Stir in French onion soup and water.
Warm frozen peas in a small, microwave-safe bowl in the microwave for 1 minute. Stir peas into the beef and soup mixture.
Pour the meat and soup mixture into the bottom of a glass casserole dish. Spread potatoes over the top using a rubber spatula. Top with remaining Cheddar cheese and sprinkle with more pepper.
Bake in the preheated oven until hot and bubbly, about 20 minutes.
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