Whisk the egg in a large bowl, then stir in the panko, ketchup (or tomato paste), Dijon, Worcestershire, salt and a few grinds of black pepper. Add the ground beef and combine gently until evenly mixed, being careful not to overwork the meat.

Shape the mixture into 4 (or up to 6) oval patties about 1/2-inch thick, pressing to form even shapes so they cook uniformly.

Heat 1 tablespoon of the oil in a large deep nonstick skillet over medium-high. Add the patties and brown on both faces until cooked through and an instant-read thermometer reaches 150–155°F. Work in batches if needed, and transfer finished patties to a plate.

Pour off excess fat from the skillet, wiping away any large burned bits with a paper towel, then reduce heat to medium and add the remaining oil if the pan looks dry.

Add the sliced onion and cook until softened and beginning to brown at the edges, about 3–4 minutes. Stir in the mushrooms and continue cooking until they release their liquid and become tender. Season with a pinch of black pepper.

Pour in the beef broth and add the tablespoon of ketchup (or paste), soy sauce, Worcestershire and Dijon, stirring to combine and scrape up any browned bits from the pan.

Whisk the cornstarch with the water until smooth, then pour the slurry into the skillet and stir for a minute or two until the sauce thickens. Add a few drops of browning sauce if you want a deeper color.

Taste the gravy and adjust salt and pepper as needed. Return the cooked patties to the skillet and spoon the mushroom-onion sauce over them to heat through and meld flavors.

Garnish with chopped parsley and serve the Salisbury steak and gravy over mashed potatoes while hot.