Heat a frying pan with the avocado oil and shallot. Add the broccoli florets and shredded carrots to the pan. Cover and cook 5 minutes, stirring occasionally until broccoli is tender.
While the broccoli cooks, add the egg white to a separate frying pan. Fry the egg white 3-5 minutes. It will look like a pancake when finished. Remove from the pan and transfer to a cutting board to cool.
Remove the cover from the broccoli, add the cauliflower rice, ginger and coconut aminos. Stir to combine, coating the cauliflower rice with the coconut aminos.
Roughly chop the egg white then add to the frying pan. Stir again.
Once the cauliflower rice has softened, make a well in the center of the frying pan. Crack the whole egg in the well. Cover and cook 3-4 minutes more until the egg sets up.
Remove the cover, sprinkle with everything bagel seasoning, add sliced green onions on top and serve immediately.