In large bowl, mix ground beef, breadcrumbs, egg, 2 tablespoons Worcestershire sauce, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1 teaspoon salt, and ½ teaspoon pepper until just combined.
Form into 4 oval patties about ¾ inch thick. Make indentation in center with thumb.
Heat oil in large skillet over medium-high heat. Cook patties 4-5 minutes per side until browned and cooked through (160°F). Transfer to plate.
Reduce heat to medium. Add butter to skillet. Add sliced onions, cook 10-12 minutes until caramelized, scraping up browned bits.
Sprinkle flour over onions, stir constantly for 1-2 minutes until absorbed.
Gradually whisk in beef broth, 1 tablespoon Worcestershire sauce, ½ teaspoon garlic powder, ½ teaspoon onion powder, ½ teaspoon salt, and ¼ teaspoon pepper.
Bring to simmer, cook 3-4 minutes until thickened. For thicker gravy, whisk in cornstarch slurry.
Return patties to skillet, spoon gravy over top. Cover, simmer on low 10 minutes.
Serve hot over mashed potatoes or rice with generous gravy.