In a large wok or lidded skillet, cover the broccoli with 2 cups water. Bring to a simmer over high heat, reduce to medium, then cover and cook until vibrant and tender, 1-2 minutes. Drain in a colander. Rinse and dry the skillet.
Meanwhile, whisk together the egg white, cornstarch, and sea salt in a large mixing bowl until smooth. Add the chicken and toss to combine.
Heat 1 tablespoon of the coconut oil in the cleaned skillet over high heat. When hot, add the chicken in an even layer. Cook until golden brown on the first side, about 2 minutes, then stir fry until the chicken is cooked through, about 4 minutes more. Transfer to a bowl and set aside.
Add the remaining vegetable or coconut oil and stir fry the peppers and white scallions until lightly charred, 2 minutes. Stir in the garlic and cook until fragrant, 1 minute.
Add the chicken back to the pan, along with the tamari, toasted sesame oil, honey, and sesame seeds. Simmer until the sauce has thickened, 2 minutes. Stir in the broccoli and green scallions. Serve over brown rice or quinoa.
