"I've loved shrimp wontons with noodles since I was a child. It's a typical Cantonese (Southern Chinese) recipe and is found in most tea cafes in Hong Kong. Most of the time wontons contain pork but I prefer those with shrimp only."
Soak rice noodles in a bowl of cold water until softened, about 10 minutes. Drain.
Bring a pot of water to a boil. Add noodles; cook, stirring occasionally, until tender, about 5 minutes. Drain.
Place shrimp on a flat work surface; pound with a meat tenderizer until a thick paste forms. Mix in sesame oil, salt, and pepper.
Place a wonton wrapper diagonally on a flat work surface. Add a spoonful of shrimp paste above the center of the wrapper. Dip a finger in egg white and dab it on the top corner. Fold top corner over to just cover the shrimp paste. Dab egg white on the fold; overlap left and right corners in the center. Repeat with remaining wrappers and shrimp.
Bring chicken broth and water to a boil in a large pot. Add wontons. Cook over medium-high heat until wontons float to the surface, about 5 minutes.
Divide noodles among serving bowls; sprinkle scallions on top. Divide wontons among bowls. Cover with hot broth.