In a large mixing bowl, combine the ground beef, breadcrumbs, milk, chopped onion, minced garlic, egg, Worcestershire sauce, salt, and pepper. Mix until well combined.
Divide the mixture into four equal portions and shape them into oval patties, about 1/2 to 3/4 inch thick.
Heat a large skillet over medium-high heat. Add a little oil to the skillet if needed. Place the hamburger steaks in the skillet and cook for about 4-5 minutes on each side, or until browned and cooked through. Remove the steaks from the skillet and set aside.
In the same skillet, add the butter for the gravy. Once melted, sprinkle in the flour and whisk continuously to form a roux. Cook for 1-2 minutes until the roux is golden brown.
Slowly pour in the beef broth and milk, whisking constantly to prevent lumps from forming. Bring the gravy to a simmer and cook for 2-3 minutes, or until it thickens.
Season the gravy with salt and pepper to taste. If the gravy is too thick, you can add a little more broth or milk to adjust the consistency.
In another skillet, melt the butter for the onions over medium heat. Add the sliced onions and cook, stirring occasionally, until they are caramelized and golden brown, about 15-20 minutes. Season with salt and pepper to taste.
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