In a large sauté pan, heat coconut oil over medium heat. Add mushrooms to pan and allow to cook down to release moisture before stirring, about 4-6 minutes. Add garlic and ginger and sauté to incorporate, about 2-3 minutes.
Add the kale and drizzle in the mushroom broth. Sprinkle in salt and pepper to taste. Using tongs, turn to coat then cover and simmer 3 to 5 minutes. Serve and enjoy!