Increase the heat to high and return the skillet to the burner.
Add 1 tbsp. oil, pick up the pan, and carefully swirl it to coat the bottom and sides.
If the oil smokes immediately when added, your pan is too hot; take the pan off the burner and let it cool for a few minutes; once cool enough to handle, wipe the oil out with paper towels and start again.
Add the ginger and red pepper flakes, stir-fry until fragrant, about 10 seconds.
Add the carrots and stir-fry until bright orange, about 1 minute.
Add the peas and corn and stir-fry until heated through, about 30 seconds.
Drizzle in the remaining 1 tbsp. of oil.
Add the rice and scallions, then stir-fry for 2 minutes.
Break up the rice with the spatula until the rice is heated through and combined with the vegetables.
Stirring with a thin metal spatula will help, but expect some of the rice to stick to the pan since you are not using a wok or nonstick pan.
Drizzle the tamari or soy sauce and sesame oil around the edge of the skillet.
Sprinkle the salt and pepper over the rice and stir-fry until the seasonings are completely incorporated, about 10 seconds.
Lower the heat to medium.
Use the spatula to push the fried rice to one side of the skillet.
Pour the beaten egg into the empty space and scramble until cooked.
Toss the egg with the rice.
Return the cooked chicken to the rice, add the nuts if using, and stir to combine.