Reduce heat to medium. Pour off all but 4 tablespoons of drippings (or if you don’t have 4 tablespoons, supplement with butter).
Add onion and mushrooms. Cook until onions turn translucent and mushrooms begin to brown, about 4-5 minutes. Add thyme and cook an additional minute.
Sprinkle flour over vegetables, stirring continuously. Cook for 1-2 minutes. Add in red wine, stirring continuously, creating a paste. About ½ cup at a time, add beef broth, stirring to ensure a smooth texture. Do not add all the liquid at once.
Once all the broth is incorporated, add in tomato paste, Worcestershire sauce, Dijon, salt, and pepper.
Return patties to gravy and cover with lid. Reduce heat to medium-low and cook until patties are cooked through and gravy is thickened, about 5-6 minutes. Stir occasionally to ensure gravy doesn’t overthicken. (You may thin out with a tablespoon or two of beef broth or water.)
Remove lid, stir in parsley, and serve over rice or mashed potatoes.