1. For the salisbury steak: Peel and finely mince onion. Separate the egg and set the white aside for another use.
2. In a large mixing bowl, add ground beef, garlic, and 1/2 of the onion. Stir to combine. Fold in egg yolk, pepper, and 1/2 of the salt. Mix until well combined.
3. Form the meat mixture into patties and set aside while you prepare the sauce.
4. Bring broth, thyme, and remaining salt to full boil over a medium-high heat.
5. Reduce to medium heat and keep at a gentle boil until sauce is reduced by half. While sauce reduces, prepare steaks.
6. Heat half the coconut oil in a pan over medium-high heat. Cook the remaining onions until they begin to soften.
7. Remove the onions, add the mushrooms, and continue sautéing the mushrooms until soft. Remove and set aside.
8. Heat remaining oil in the skillet and add the patties, searing on both sides until nice and brown on the outside but still pink in the center.
9. In a small bowl, mix the arrowroot powder and water together and incorporate into the sauce, then remove sauce from heat.
10. Smother the patties with sautéed mushrooms and onions. Top with the sauce. Continue to simmer over a moderately low flame until the steaks are cooked through.
11. For the kale: Meanwhile, remove and discard kale stems. Mince the leaves.
12. Steam kale in a saucepan with a small amount of filtered water until tender and bright green. Pour off any liquid and toss kale with olive oil.
13. Serve salisbury steak topped with the mushroom and onion sauce alongside the sautéed kale.