In a bowl, combine breadcrumbs and milk; let sit 3 minutes to form a panade.
Add ground beef, minced onion, garlic, egg, Worcestershire, ketchup, salt, and pepper. Mix gently until just combined.
Shape the mixture into 6 oval patties about 0.75 inch thick.
Heat olive oil in a large skillet over medium-high. Sear patties 3 to 4 minutes per side until well browned. Transfer to a plate.
Reduce heat to medium. Add butter, sliced mushrooms, and onions to the skillet; cook, stirring, until softened and lightly browned, 6 to 8 minutes.
Stir in tomato paste and Dijon; cook 30 seconds. Pour in beef broth and Worcestershire, scraping up browned bits.
Whisk cornstarch with water to make a slurry. Stir into the skillet and bring to a simmer until slightly thickened.
Return patties and accumulated juices to the pan. Cover and simmer on medium-low until patties are cooked through (160°F) and gravy is silky, 8 to 10 minutes. Adjust salt and pepper to taste.
Garnish with parsley and serve with mashed potatoes or buttered noodles.
Notes
For extra tenderness, avoid overworking the meat. Make ahead: Form patties up to 24 hours in advance and refrigerate; reheat gently in the gravy, adding a splash of broth as needed.