Preheat a wok or large skillet over medium-high heat with a bit of oil. Add the broccoli florets and sauté until they are golden brown. Remove from the wok and set aside.
In the same wok, add a little more oil if needed and pour in the beaten eggs. Scramble them quickly, then immediately remove and set aside.
Add the sesame oil and cold rice to the wok. Break up any clumps of rice with a spatula. Allow it cook untouched for a minute or two to get some crispy bits on the bottom.
Add the cooked chicken, broccoli, and scrambled eggs back to the pan. Stir everything together. Add the soy sauce and toss until everything is evenly coated and heated through (about 2–3 more minutes).
Top the fried rice with green onions or sesame seeds if you like, and serve hot!