Combine soy sauce, garlic, sugar, and chili flakes in a small bowl; stir and set aside.
Heat 1 Tbsp. of the oil in a large skillet over medium-high. Once hot, add broccoli; cover and cook 5 minutes, uncovering occasionally to stir, under crisp-tender. Add green onion and season with a pinch of salt; cook 1 to 2 more minutes, uncovered, until soft. Transfer veggies to a bowl.
Heat remaining 1 Tbsp. oil in pan. Pour in whisked eggs and cook, stirring constantly, with a rubber spatula for 30 to 45 seconds, until just cooked through. Add cooked rice and soy sauce mixture; stir well to combine. Cook, undisturbed, until rice is slightly crisped on one side, about 3 minutes.
Return broccoli and green onion to pan, and stir in edamame. Toss well to combine; turn off heat.
Prepare Turmeric-Tahini Sauce by combining tahini, vinegar, sugar, turmeric, sesame oil, ginger, and salt in a bowl; stir with a whisk. Gradually whisk in up to 2 1/2 Tbsp. warm water to reach desired consistency.
Divide fried rice evenly into 4 bowls and drizzle with Turmeric-Tahini Sauce. Finely chop the leftover whites of the green onion and sprinkle overtop as garnish, if desired. Top with toasted sesame seeds and/or chili oil.