Mince cauliflower into very small crumbled pieces, resembling the size of rice or larger because the cauliflower will shrink as it cooks.
In small bowl, whisk the egg and then set aside.
Heat large skillet on medium high heat. Add olive oil, then add onion and garlic. Cook until soft and translucent.
Add cauliflower and sauté until tender, but not mushy soft. Add the peas and carrots and stir until combined.
Add the beaten egg, soy sauce, sesame oil and black pepper. Stir until the egg coats all of the cauliflower and becomes cooked.
If needed, add additional kosher salt to taste. Add green onions and stir until everything is combined.
In a small bowl, whisk together the broth, soy sauce, hoisin sauce, sesame oil and cornstarch until combined.
In a large nonstick skillet, heat the olive oil over medium heat. Add the broccoli and stir fry for 4-5 minutes until it is bright green and tender crisp. If you like it more well cooked, continue cooking for a couple more minutes. Add the garlic and continue stir frying for another minute or so. Pour the sauce over top of the broccoli and stir well to coat the broccoli with the sauce. Simmer for a minute or two until the sauce is heated through. Serve immediately.