Form the beef into patties and fry in the oil over medium heat for about 3 minutes on each side or until cooked to your liking.
Meanwhile, bring the broth to a simmer in a small saucepan over medium-high heat and stir in the salt and pepper.
Combine the arrowroot and cold water in a separate dish to make a thick slurry, then slowly pour it into the simmering broth, stirring constantly until a thick gravy forms.
Once the beef patties are done cooking, remove from the pan and set aside. Crack the eggs into the pan, season with salt and pepper to taste, and cook until the whites are solid but the yolks are still runny.
Place 1 cup of cauliflower rice on each of four plates, then top each with a beef patty and about 1 cup of gravy before placing a fried egg on top.