Birthday is a big day in one's life. In the old days, Chinese people would eat a bowl of "长寿面 (cháng shòu miàn, literally "longevity noodles", a type of noodles eaten specially on one's birthday – they're also called birthday noodles)" rather than a birthday cake. As this type of noodles is "长 (cháng, long)" and "瘦 (shòu, thin)", and the pronunciation of the two words is the same to the Chinese word "长寿 (cháng shòu)", longevity. "长寿面" (cháng shòu miàn), means wishing the person celebrating a birthday a long life.
Chinese people often put an egg in the "长寿面 (cháng shòu miàn)" because egg yolk is round, and roundness stands for "圆满 (yuán mǎn, to be satisfactory, or perfect)" and a symbol of new life in Chinese culture. The ways of making "长寿面 (cháng shòu miàn)" are quite diverse across different regions. The birthday noodles are usually longer. The person that celebrates the birthday should finish a string of noodle at one go while eating "长寿面 (cháng shòu miàn)", and he/she should not bite off the noodle before slurping it up completely.
About 2,100 years ago, Emperor Wu was keen on physiognomy, fortune telling by studying facial features (相术-xiàng shù). He was convinced that a person's destiny could be determined by his/her looks. Emperor Wu once chatted with the ministers and said, "A book mentions that the longer a person's groove between upper lip and nose (人中-rén zhōng) is, the longer he would live." Then one of the ministers began to laugh and said, "Peng Zu (彭祖, a legendary long-lived figure in China from 1900 to 1066 BC) has lived for 800 years, and how long could his groove be?" In Chinese, another saying for "脸 (liǎn)" (face) is "面 (miàn)". Because of this legend, Chinese people gradually cultivate the habit of eating "长寿面 (cháng shòu miàn)" on birthday.
That is just an interesting tale of course. Historians have never factually proved the tradition of eating "长寿面 (cháng shòu miàn)" originates from the story of Emperor Wu. "长寿面 (cháng shòu miàn)" in China means a happy wish for the future. Chinese people hope that the person celebrating a birthday can live longer after eating a bowl of "长寿面 (cháng shòu miàn)".