Mix the beef, breadcrumbs, egg, milk, 2 tsp Worcestershire, salt and 1/2 tsp pepper just until combined.
Shape the mixture into six wide oval patties about 3/4 inch thick.
Heat the oil in a skillet over medium-high heat and brown the patties in two batches, 2 minutes per side; transfer them to a 6-quart slow cooker.
Spread the onion and mushrooms over the patties and add the broth, remaining Worcestershire and remaining pepper.
Cover and cook on low until the patties reach 160°F and the onions are soft, 4 1/2 to 5 hours.
Transfer the patties to a platter and switch the cooker to high.
Whisk the cornstarch with the cold water, stir it into the mushroom liquid and cook until thick and glossy, 8 to 10 minutes.
Spoon the mushroom gravy over the patties.