Preheat oven to 375 degrees Fahrenheit (190 degrees Celsius).
In a large mixing bowl, combine ground beef, breadcrumbs, egg, garlic powder, onion powder, Worcestershire sauce, salt, and black pepper until just incorporated.
Divide the beef mixture into 4 equal portions and shape into oval patties approximately 3/4-inch thick.
Heat vegetable oil in a large skillet over medium-high heat. Sear the patties for 3-4 minutes per side until a brown crust forms, then transfer them to a 9x13 inch baking dish.
In the same skillet, melt butter and add sliced mushrooms and onions. Sauté for 5-7 minutes until the onions are translucent and mushrooms are browned.
Pour the beef broth into the skillet, scraping the bottom to release browned bits. In a small cup, whisk cornstarch and water to create a slurry and stir it into the broth.
Simmer the gravy for 2-3 minutes until thickened, then pour the mixture over the patties in the baking dish.
Bake in the preheated oven for 20 minutes.
Remove from oven, sprinkle shredded cheddar cheese evenly over each patty, and return to the oven for 5 minutes until the cheese is fully melted and bubbly.
Serve warm with the gravy spooned over the top.