Combine the ground beef, beaten egg, breadcrumbs, onion soup mix, milk, and Worcestershire sauce in a large bowl and mix thoroughly by hand until well incorporated.
Shape the meat mixture into eight even patties.
Pour the flour onto a small plate and coat each side of the patties with flour, shaking off any extra.
Heat the vegetable oil in a large skillet over medium-high heat and quickly brown the patties on both sides without cooking them through completely.
Prepare your slow cooker by spraying it lightly with cooking spray, then carefully layer the patties inside, stacking if necessary.
In a separate bowl, whisk together the beef broth, au jus gravy mix, minced garlic, Worcestershire sauce, and dijon mustard until combined.
Pour the gravy mixture evenly over the patties in the slow cooker.
Cook on low for 4 to 5 hours, or on high for 3 to 4 hours, until the patties are cooked through and reach at least 165°F internally; longer cooking will make the patties more tender.
Remove the patties from the slow cooker and place them on a serving dish.
Transfer the cooking liquid to a large skillet and heat over medium until it starts to simmer.
In a small bowl, whisk together the water and cornstarch to create a slurry, then slowly whisk this into the simmering gravy until it thickens, about 1 to 2 minutes.
Either serve the patties immediately topped with the thickened gravy or return them to the slow cooker and pour the gravy over them, keeping warm until serving.
Garnish with fresh chopped parsley if desired and serve with mashed potatoes, egg noodles, or rice.
