Make small slit in each shrimp; pull tail through.
Pour hot water over spinach to wilt; drain.
Divide and arrange shrimp, spinach, mushrooms, and water chestnuts in six 6-ounce custard cups or Chawan-Mushi cups.
Combine eggs, broth, and salt; pour into cups.
Cover each cup with foil; set on wire rack in Dutch oven or deep skillet.
Pour hot water around cups to depth of 1 inch on cup sides; cover Dutch oven or skillet.
Over medium heat bring water to simmering.
Reduce heat; cook till knife inserted off-center comes out clean, about 10 minutes