Prepare vegan egg replacer:
Prepare the egg replacer according to package directions. Set aside.
Make the patties:
Into a large mixing bowl, add vegan ground beef, bread crumbs, egg replacer mixture, milk, and 1/2 package onion soup mix, Worcestershire sauce, and black pepper. Use your hands to mix well, until all ingredients are fully incorporated, then form into 5 patties.
Heat a large skillet over medium heat. Add patties and cook until browned, 3-5 minutes on each side. Remove patties from skillet and set aside.
Make the sauce:
Place the same skillet used for cooking the patties over medium-high heat then add butter. When butter is melted, add mushrooms and onions. Sauté 3-5 minutes, until tender. Add garlic and saute 1 minute more.
Stir in flour and remaining 1/2 package onion soup mix. Gradually add vegan beef-style broth, stirring continuously. Reduce heat to medium and simmer, continuing to stir until thickened, about 3 minutes. Season to taste with salt and pepper,
Put it all together:
Add patties back into the skillet with the gravy. Reduce heat to low and simmer 25-30 minutes. Serve hot.