In a large bowl, combine beef, egg, bread crumbs, garlic powder, onion powder, and paprika. Season with salt and pepper. Divide beef mixture into 4 patties, then flatten to ½” thick oval patties.
In a large skillet over medium heat, heat oil. Add patties and cook until golden and cooked through, 6 to 8 minutes per side. Remove from skillet and set aside to keep warm.
To same pan, melt butter. Add mushrooms and onions and cook until softened, 5 minutes. Add flour and toss to coat veggies. Slowly whisk in broth, then add Worcestershire. Bring to a boil, then reduce heat to a simmer and let simmer until thickened, about 5 minutes. Season with salt and pepper.
Return steaks to skillet and spoon sauce over. Heat until warmed through.