In a large bowl, combine ground beef, beaten egg, breadcrumbs, onion soup mix, milk, and Worcestershire sauce until evenly mixed.
Divide this meat mixture into 8 equal portions and shape each into a patty.
Pour the flour onto a plate and coat both sides of each patty, shaking off any extra flour.
Heat vegetable oil in a skillet on medium-high heat and sear the patties in batches until they have a golden crust but are not fully cooked.
Spray a 6-quart slow cooker with cooking spray and place the patties inside, layering if necessary.
Mix together beef broth, au jus gravy mix, minced garlic, Worcestershire sauce, and dijon mustard in a bowl, then pour this over the patties in the slow cooker.
Cook on low for 4-5 hours or on high for 3-4 hours until the patties reach 165°F internally and become tender.
Remove the patties from the slow cooker and set aside.
Transfer the cooking liquid to a skillet and bring it to a simmer over medium heat.
Whisk together water and cornstarch in a small bowl, then gradually add this mixture to the simmering gravy, stirring constantly until it thickens, about 1-2 minutes.
Serve the patties immediately with the thickened gravy spooned over them, or return them to the slow cooker with the gravy and keep warm.
Garnish with fresh chopped parsley if desired and enjoy with mashed potatoes, egg noodles, or rice.
