Make the bang bang sauce. Whisk together the mayonnaise, sweet chili sauce, sriracha, and rice vinegar in a small bowl. Set aside it needs no cooking and can be made a day ahead if you want to save a step later.
Coat the chicken. Mix the cornstarch, flour, salt, and pepper in a shallow bowl. Dip each piece of chicken in the beaten egg, then toss in the cornstarch mixture until fully coated, pressing lightly so the coating sticks.
Fry the chicken in batches. Heat about ½ inch of oil in a skillet over medium-high heat until it reaches roughly 350°F (a cube of bread should sizzle and brown in about 30 seconds). Fry the chicken in batches of 6–8 pieces for 4–5 minutes, turning occasionally, until deeply golden and cooked through. Don’t crowd the pan, or the pieces will steam each other instead of crisping.
Rest the chicken before saucing it. Transfer the fried chicken to a wire rack not a paper-towel-lined plate and let it rest, uncovered, for 2 full minutes before tossing it in the sauce. This short rest matters more than it looks like it should: residual heat keeps crisping the coating for another minute or two after it leaves the oil, and a paper towel traps steam underneath the chicken that softens the bottom of the crust right as it’s setting. Skip the rest and the coating starts going soft before the sauce even touches it.
Toss the chicken in bang bang sauce. Once rested, toss the chicken with the bang bang sauce until evenly coated. Set aside while you make the rice the crunch holds for a good 10–15 minutes even sauced, thanks to the rest in the last step.
Scramble the eggs separately. Heat 1 tablespoon of oil in a large skillet or wok over medium-high heat. Pour in the beaten eggs and scramble into small curds, about 1 minute, then push to one side of the pan (or remove entirely if your pan is small).
Fry the rice. Add the remaining oil to the pan along with the garlic and the white parts of the green onions. Cook for 30 seconds until fragrant, then add the cold rice, breaking up any clumps with your spatula. Stir-fry for 3–4 minutes, pressing the rice against the hot pan occasionally, until it’s heated through and the edges of some grains start to look slightly crisp. Pro tip: resist the urge to stir constantly letting the rice sit against the pan for a few seconds at a time is what gives you those slightly crispy edges instead of uniformly soft grains.
Finish the rice. Add the peas and carrots, soy sauce, and oyster sauce, then fold in the scrambled egg. Toss everything together for another minute until evenly combined and heated through.
Serve. Divide the fried rice into bowls, top with the sauced bang bang chicken, and finish with the sliced green onion tops.