Heat one Tablespoon of oil in a large skillet over medium heat. Add the onion slices and cook for 5 to 7 minutes, until almost translucent. Reduce heat to low, and continue cooking for an additional 10 minutes, stirring occasionally until golden brown and caramelized.
Add the garlic and cook for one minute, just until fragrant. Remove from skillet and place in a bowl.
Pour one more Tablespoon of oil into the skillet. Season the ground beef patties with salt and pepper, then place in the hot skillet. Cook until browned and cooked through, about 5 minutes per side depending on thickness. Remove the patties to a plate to rest and cover with foil.
Place the onions back into the skillet and add the soy sauce (coconut aminos), fish sauce, beef stock to the skillet and bring almost to a boil. Reduce heat to medium-low. Scoop out two Tablespoons of the hot liquid from the skillet and mix it with the cornstarch (arrowroot/glucomannan/xanthan gum) in a small bowl.
Whisk the cornstarch mixture into the skillet. Continue to simmer until gravy thickens, about 5 or 6 minutes.
Heat two teaspoons of oil in a non-stick skillet over medium-high heat. Add eggs and cook undisturbed for 3 to 4 minutes, until the white is cooked through the the yolk is still loose.
Place one cup of rice on each plate and top with a burger patty. Ladle the gravy over the patty, top with an egg and garnish with green onions.
I used beef bone broth for a more intense flavor, but a good quality beef stock works well too.
Whole30/Paleo/Keto substitute cauliflower rice and coconut aminos for the soy sauce.
Substitute Glucomannan, Xanthan Gum, or arrowroot starch for the cornstarch if needed.
Shoyu would be used in Hawai’i, but it is difficult to find on the mainland. Use a good quality tamari or soy sauce for the best flavor.