In a medium bowl mix the soy sauce into the peanut butter, then whisk in all the other sauce ingredients and set aside.
Heat up sesame oil in a wok on a medium heat, then whisk one of the eggs and pour it into the wok. Roll the pan to spread the egg out a bit, and cook to set. Flip over for a few seconds, then transfer to a plate, roll up and cut into thin strips. Repeat with additional eggs and set aside.
Add more oil to the pan, then add the garlic and ginger. Cook for a minute, then add the chicken. Stir fry for a couple more minutes or until just cooked through.
Add the bok choy to the pan, stir fry for another couple of minutes until wilted and then add the noodles. Pour in the sauce at this point and combine all the ingredients.
Before serving add the beansprouts, tomatoes and eggs and combine well once again to warm. Add a splash of water if you think the dish needs it.
Serve the noodles immediately, topping with the lime!