Heat 2 tablespoons sesame oil in a wok or large skillet over medium-high heat. Toss in pork and stir until thoroughly coated. Add cauliflower rice, broccoli florets, mushrooms, celery, and garlic. Cook, stirring frequently, until pork is slightly pink in the center, 5 to 7 minutes.
Push pork and cauliflower mixture to one side of the wok. Pour beaten eggs into the empty side and stir the egg until cooked and scrambled, about 2 minutes. Mix the pork and cauliflower mixture into the egg. Stir in tamari, green onions, and remaining 1 tablespoon sesame oil. Stir fry until heated through, about 2 more minutes.