Brown ground beef in a skillet over medium-high heat.
If serving four, add the ground beef to the bottom of one small casserole dish. If serving two, add the ground beef to two smaller casserole dishes to eat one now and freeze one for later.
Prepare the brown gravy according to the package directions.
Spoon the gravy over the ground beef. Do not cover the meat. The gravy should come to just under the top of the meat. Save the remainder to serve tableside if desired.
Place the frozen vegetables in an even layer over the ground meat mixture.
Top the vegetables with grated cheese in an even layer.
Prepare the instant mashed potatoes according to the package directions.
Place the mashed potatoes over the cheese to just over the top of the baking dish.
If freezing one, cover it tightly with plastic wrap, then cover it with aluminum foil.
Bake the remaining casserole for 30 mins at 350 degrees f.
Enjoy this dish piping hot, with a pat of (optional) butter on top, right from the oven.