Fill a large pot of water. Place the potatoes into the pot and bring to a boil. Boil for 15-20 minutes until cooked.
While the potatoes boil, brown the ground beef over medium-high heat in a large frying pan. If necessary, drain excess fat.
Add the brown gravy mix and water and simmer for 5 minutes to reduce and thicken. Remove the cooked ground beef from the heat and set aside.
Defrost the vegetables in the microwave. Drain well.
Transfer the ground beef mixture to a 9x13 casserole dish. Spread the vegetables in an even layer on top of the meat.
Drain the potatoes and return them to the same pot. Add butter, milk, salt, and pepper, and cover, off heat, for 2 minutes to let the butter melt. Mash the potatoes thoroughly with a potato masher until smooth and creamy.
Top the meat and vegetables with the mashed potatoes, spreading them to the edge of the pan and leveling the top of the potatoes so that they are smooth. Use a fork to create a pattern on the top of the potatoes.
Bake the Shepherd’s Pie at 400º Fahrenheit for 30 minutes. Remove from the oven and rest for 5 minutes, then serve.