In a large mixing bowl, combine the ground beef, finely chopped onion, breadcrumbs, beaten egg, garlic powder, salt, and black pepper. Mix until all ingredients are evenly incorporated.
Shape the meat mixture into four equal-sized oval patties, about 1 inch thick, and set them aside.
In a large, oven-safe skillet, heat 1 tablespoon of oil over medium heat. Add the hamburger patties to the skillet and brown them on each side for approximately 3-4 minutes. Remove the patties from the skillet and set them aside.
In the same skillet, layer the thinly sliced potatoes evenly across the bottom. Pour the cream of mushroom soup and beef broth over the potatoes. Stir gently to combine.
Carefully arrange the browned hamburger patties atop the potato mixture. Scatter the frozen peas and carrots over everything.
Cover the skillet with a lid or aluminum foil and place it in the preheated oven. Bake for 25 minutes.
After 25 minutes, remove the lid or foil and sprinkle the shredded sharp cheddar cheese evenly across the top. Return the skillet to the oven and bake uncovered for an additional 10-15 minutes.
Once done, remove the skillet from the oven and let it cool for a few minutes before serving. Garnish with chopped fresh parsley if desired.
Notes
Serve directly from the skillet for a rustic look.