In a large mixing bowl, combine the ground beef, breadcrumbs, egg, Worcestershire sauce, onion powder, garlic powder, salt, and pepper until just incorporated.
Divide the mixture into 4 equal portions and shape into oval patties approximately 3/4-inch thick.
Heat olive oil in a large skillet over medium-high heat. Brown the patties for 3 to 4 minutes per side, then remove from the pan and set aside.
Lower heat to medium and melt butter in the same skillet. Add the sliced onions and sauté for 8 to 10 minutes until caramelized and soft.
Sprinkle flour over the onions and stir constantly for 1 minute to cook out the raw flour taste.
Gradually whisk in the beef broth and Dijon mustard, scraping the bottom of the pan to deglaze and release browned bits.
Return the patties and any accumulated juices to the skillet. Simmer for 5 to 7 minutes until the gravy has thickened and the meat reaches an internal temperature of 160°F.
Adjust seasoning with salt and pepper to taste before serving.