In a large mixing bowl, combine the ground beef, egg, tomato paste, yellow mustard, Worcestershire Sauce, garlic powder, breadcrumbs, pepper, and salt. Mix well to combine all of the ingredients. Shape the meat mixture into four oval-shaped patties.
Heat a large skillet over medium heat for about a minute, then add the butter. Place the meat patties in the skillet and cook them for about 4 to 5 minutes on each side, or until they’re well-browned. Remove the patties from the skillet and set them aside.
Prepare the gravy: add the chopped onions to the skillet and reduce the heat to medium-low. Cook the onions until they are translucent and caramelized, about 15 to 20 minutes. Sprinkle 2 to 3 tablespoons of arrowroot over the caramelized onions and stir to coat. (Use 2 tablespoons of arrowroot if you like your gravy on the thinner side or 3 tablespoons for a thicker gravy). Cook the coated onions for another minute or so. Add the dried thyme and cook until fragrant, about 30 seconds. Gradually stir in the beef broth and coconut aminos and raise the heat back to medium.
Add the seared patties back to the skillet. Bring to a gentle simmer, cover, and cook the patties for 10 to 15 more minutes, or until they’re cooked through. Taste the gravy for seasoning (it will thicken more as it cools). Remove the Salisbury steaks from the heat and serve them warm.