Place the onion and garlic in a food processor with 1 teaspoon water and purée, until the onion and garlic is very well blended. If you don't have a food processor, you can just mince everything together as finely as you can.
Gently mix the blended onion and garlic with the ground beef, panko, egg, ketchup, 1 teaspoon Worcestershire, and 1 teaspoon dijon until completely incorporated. Divide the mix into 4 and shape into oval patties.
Sear the patties: Heat a bit of oil in a skillet over medium-high heat. Add the patties and sear until the patty crusts and browns, about 3-4 minutes per side. Flip and cook the other side until it browns. Remove from the pan and set on a plate.
Make the gravy: In the same skillet, add the butter and melt over medium heat. Add the mushrooms and cook, stirring, until the mushrooms are golden, 2-3 minutes.
Sprinkle on the flour and cook for 30 seconds, stirring to coat the mushrooms in flour. Slowly stream in the beef stock, stirring. Stir in the remaining 2 teaspoons Worcestershire and 1 teaspoon of dijon.
Add the steaks, along with any juices on the plate, back into the pan with the gravy and bring to a simmer. Cook, uncovered, for 5-7 minutes, or until the gravy thickens. Remove from the heat, taste, and season the gravy with salt and pepper.