Add the cooked, chilled rice to a large bowl with the mayo and stir to coat.
Add the oil and butter to a wok over medium-high heat. Once the butter is mostly melted, add the onion and cook until the onion is starting to soften but not turning color, about 2 to 3 minutes, tossing occasionally. Stir in the garlic and ginger, and cook 30 seconds, tossing it around.
Add the rice to the wok, tossing it around with the onion mixture, and spread it out in an even layer. Let it cook for 30 seconds to 1 minute, and then flip it around with a metal spatula so the other side cooks. Repeat this process for about 3 to 5 minutes, until the rice is warm throughout and starts to take on a little color.
Make a well in the center of the rice. Pour the egg into the well and let it cook until it sets on the bottom, about 1 minute. Flip the egg around with a metal spatula so the uncooked part cooks. When the egg is about 3/4 of the way cooked, toss it through the rice and spread the rice out in an even layer.
Add 3/4 of the scallion, the salt, white pepper, soy sauce, toasted sesame oil, and sesame seeds. Toss everything together to combine.
Remove from the heat. Sprinkle the remaining 1/4 of the scallion on top, along with more sesame seeds if desired.
Serve the fried rice along with Yum Yum Sauce to drizzle on top if desired.