Form the Patties: In a large bowl, combine ground beef, egg, breadcrumbs, garlic powder, onion powder, and paprika. Season with salt and pepper. Divide the mixture into 4 equal portions, shaping into oval patties about ½-inch thick.
Cook the Patties: Heat olive oil in a large skillet over medium heat. Add the patties and cook, flipping once, until browned and cooked through (about 6–8 minutes per side). Transfer to a plate and keep warm.
Make the Gravy Base: In the same skillet, melt butter over medium heat. Add sliced mushrooms and onions, cooking until softened (about 6–8 minutes). Stir occasionally to prevent sticking.
Thicken with Flour: Sprinkle flour over the vegetables, tossing to coat. Cook for 1–2 minutes to eliminate the raw flour taste.
Build the Sauce: Gradually whisk in beef broth, making sure to scrape up any browned bits from the pan. Add Worcestershire sauce and thyme. Bring to a boil, then reduce heat to medium-low and simmer until thickened, about 5 minutes. Season with salt and pepper to taste.
Smother the Steaks: Return the patties to the skillet, spooning gravy over the top. Simmer for 1–2 minutes until warmed through.
Serve: Plate the hamburger steaks with generous scoops of gravy on top. Serve with mashed potatoes, rice, or buttered noodles.