Heat the 1 tablespoon of oil in a flat-bottomed wok or large nonstick frying pan over medium-high heat until shimmering. Add the eggs and gently scramble with a rubber spatula until just softly set, 1 to 2 minutes. Transfer to a bowl or plate and set aside.

Add the remaining 1 tablespoon oil, sausage, and onion to the pan and cook, breaking up the meat with a wooden spoon into small pieces, until the sausage is cooked through and the onion is tender, about 5 minutes. Add the rice and stir-fry until heated through, about 3 minutes. Use your spatula to flatten out and break up any clumps.

Add the tamari or soy sauce and salt, season with pepper, and cook for 1 minute more. Add the scrambled eggs, cheese, and peas to the pan and gently fold to combine until the cheese is melted. Taste and season with salt or soy sauce as needed. Sprinkle with the parsley and serve.