Heat oil in a nonstick pan or wok over medium-high heat.
Add the beaten eggs and scramble until just cooked. Remove from the pan and set aside.
In the same pan, add a little more oil if needed. Add the cold rice and break apart clumps.
Season with salt, sugar, and mushroom seasoning. Stir to combine.
Add soy sauce and toss the rice until evenly coated and heated through.
Return the scrambled eggs to the pan and mix well.
Stir in chopped green onions, give it a final toss, and serve warm.