In a bowl, mix together the ground beef, mustard, Worcestershire sauce, garlic powder, onion powder and 1 pinch of salt.
Heat 1 teaspoon olive oil in a skillet over medium heat.
Form the beef mixture into 4 patties, and cook each beef pattie 5 minutes per side in the skillet. You might want to put the lid on the skillet to steam the hamburger patties a little bit. The meat is done when a thermometer registers an internal temperature of 160 °F
Transfer the hamburger patties to a plate and cover them with aluminum foil to keep them warm.
Add the sliced onions to the pan you just cook the beef in. Cook the onions for about 10 minutes, until they are caramelized and deeply brown. Try to scrape up all the browned beef bits on the bottom of the pan; if the food stuck to the bottom of the pan starts blackening and burning, use a few tablespoons of beef stock to soften things up.
Stir the flour into the beef broth and pour it over the onions in the skillet. Turn the heat up to "medium-high" until the broth begins to boil and the sauce begins thicken. Turn the heat down to "medium low" and let it simmer for about 5 minutes, taking care that the sauce doesn't stick to the bottom of the pan and burn (you might need to give it a few more stirs, or add more broth.)
Last, stir in the ketchup and another pinch of salt.
Spoon the "gravy" over the ground beef patties.