In a large mixing bowl, combine the ground beef, breadcrumbs, egg, onion powder, garlic powder, 1 tsp Worcestershire sauce, 1/2 tsp salt, and 1/4 tsp black pepper. Mix gently with your hands until just combined, being careful not to overmix.

Divide the mixture into 4 equal portions and form each into a flat, oval or round patty, about 3/4-inch thick. Make a slight indentation in the center of each patty to prevent bulging during cooking.

Heat 2 tablespoons of vegetable oil in a large skillet over medium-high heat. Once hot, carefully place the hamburger steaks in the skillet, ensuring not to overcrowd. Cook for 4-6 minutes per side, or until deeply browned and cooked through to your desired doneness (internal temperature 160°F for medium-well).

Remove the cooked hamburger steaks from the skillet and set aside on a plate. Tent loosely with foil to keep them warm. Leave any accumulated pan drippings in the skillet.

While the steaks are cooking, place the peeled and cubed potatoes in a large pot. Cover with cold water by about an inch. Add a generous pinch of salt to the water.

Bring to a boil over high heat, then reduce heat to medium and simmer for 15-20 minutes, or until the potatoes are fork-tender. Drain the potatoes thoroughly in a colander.

Return the drained potatoes to the empty hot pot. Add the warmed milk, butter pieces, 1/2 tsp salt, and 1/4 tsp black pepper. Using a potato masher or an electric mixer on low speed, mash until smooth and creamy. Taste and adjust seasoning as needed. Cover to keep warm.

If using, add the sliced yellow onion to the skillet with the reserved pan drippings (or 2 tbsp fresh butter if drippings are scarce). Sauté over medium heat for 3-5 minutes until softened and lightly browned.

Sprinkle the flour over the onions (if using) and drippings in the skillet. Cook, stirring constantly, for 1-2 minutes to create a roux. This helps cook out the raw flour taste.

Gradually whisk in the beef broth, a little at a time, ensuring no lumps form. Stir in the remaining 1 tsp Worcestershire sauce. Bring the gravy to a simmer, stirring frequently, and cook for 3-5 minutes or until it thickens to your desired consistency.

Taste the gravy and season with salt and pepper as needed. If the gravy is too thick, add a splash more beef broth; if too thin, simmer a bit longer or create a small cornstarch slurry (1 tsp cornstarch mixed with 1 tbsp cold water) and whisk it in.

Place a portion of creamy mashed potatoes on each plate. Top with one or two hamburger steaks and generously spoon the rich brown gravy over the steaks and potatoes. Serve immediately and enjoy!