Combine beef with ginger, garlic, olive oil and cilantro in a bowl. Cover and refrigerate for 1-2 hours. Bring beef out of refrigerator at least 45 minutes before cooking. (If you are pressed for time, marinate at room temperature for 1 hour.)
Heat a wok or a large (12-13 inch pan) over medium heat and add half of the meat mixture. Season with sea salt and pepper. Stir fry 2 to 3 minutes, just until cooked. Remove the meat and stir fry the next batch, seasoning first with sea salt and pepper.
Heat the coconut oil in the pan over medium-high heat and cook the onion until softened, 3-4 minutes. Add the shiitake mushrooms and season with sea salt. Stir fry the onions and mushrooms until the mushrooms have softened and are cooked through, about 4-5 minutes.
Return the meat to the pan and squeeze the lime over the meat and vegetables. Toss to coat and season with sea salt and pepper to taste.