Bring a large pan of water to the boil. Add the noodles and cook following pack instructions until soft. Briefly rinse in cold water and drain well. Transfer to a large bowl, toss with the gluten free soy sauce until coated, then set aside.
To make the eggs, heat the oil in a non-stick frying pan. Add the egg mixture, swirling to evenly coat the bottom of the pan. Cook for about 2 mins, without touching, until the egg is set but just barely browned on the bottom.
Flip and cook for 15-20 secs more until the bottom is just set. Slide onto a chopping board, roll into a log and cut crosswise into thin strips. Set the egg strips aside and wipe out the pan.
Heat the oil in the pan, add the shrimp, season with salt and cook for 11/2 mins, stirring often, until the shrimp are just pink. Add the mirim and cook for 3 mins, stirring often, until cooked through. Transfer the mixture to a bowl.
For the vegetables, add the oil to the pan over medium heat. Add the carrot, and cook until slightly softened. Stir in the spinach in handfuls, adding more as it wilts. Add the scallions and noodles, and toss together.
Add the sugar, sesame oil, sesame seeds, gluten free soy sauce and a good pinch of salt. Toss well and cook for 2 mins until the noodles are heated through and glossy. Add the egg strips and shrimp, and gently toss together. Transfer to a platter and serve immediately.