In a large bowl, combine ground beef, eggs, crushed potato chips, dry mustard, garlic powder, salt, and pepper. Mix gently with your hands until fully combined; do not overmix.
Shape the mixture into 4 equal patties (about ½-inch thick). Set aside.
In a large 12-inch skillet, heat the butter and olive oil over medium-high heat. Add the patties and cook for 4 to 5 minutes per side, or until browned and cooked through to an internal temperature of 160°F.
Remove patties to a plate and carefully drain excess grease, leaving about 1 tablespoon in the skillet.
Add the sliced onion and mushrooms to the skillet. Cook, stirring occasionally, until the onions are soft and golden and the mushrooms have released their liquid and started to brown, about 6 to 8 minutes.
In a small bowl, whisk together beef broth and cornstarch until smooth.
Pour the broth mixture into the skillet with the onions and mushrooms. Add the Worcestershire sauce and stir to combine.
Bring to a gentle simmer over medium-low heat, stirring occasionally, until the gravy is thickened, about 2 to 3 minutes. If the gravy becomes too thick, add a splash of beef broth to loosen it.
Return the patties to the skillet, nestling them into the gravy. Spoon some of the gravy over the tops.
Simmer gently for 2 to 3 minutes, or until everything is heated through and the flavors have come together.
Serve hot, spooning extra onion-mushroom gravy over each patty.