Remove the beef strips from the refrigerator half an hour ahead of time to bring to room temperature. Pat the meat dry with paper towels and season with salt and freshly ground black pepper.
Heat a wok over high heat until smoking hot. Heat half the coconut oil in the pan. Add the mixed stir-fry vegetables and stir-fry for five to seven minutes until tender-crisp. Remove the vegetables from the pan and set aside on a plate.
Set the wok immediately back over the heat and add the remaining coconut oil. Place the beef strips in the pan, ensuring they don't overlap. Cook the meat for one to two minutes without stirring. Then turn the pieces over and cook for another minute until browned on all sides.
Return the cooked stir-fry vegetables to the pan with the meat. Stir everything briskly over high heat for thirty seconds so all ingredients are heated through. Taste and adjust seasoning with additional salt and pepper if needed.
Divide the beef strips and stir-fried vegetables among the plates and serve immediately.