How do the pros recover so quickly after a crash? And what can we learn from them?
Because there is no answer yet I would like to add my thoughts on this subject, from pure logic perspective and some previous reading on biking theory. Would like to hear your comments and thoughts!

Background


Generally speaking, professionals have better than average physiology which includes recovery capabilities too. Physical training is a process of constant damaging of the muscles and their recovery done with supercompensation. Professionals are in constant recovery mode since very young age.
Well-developed muscles and joints. Professionals are very flexible and muscularly developed. This is why it's recommended to do stretching, to ensure that your body can handle excessive stress / extreme positions without getting a trauma. This fact is quite obvious to me through my life experience, but studies results vary.


Working environment and culture


I believe that professionals should have a base training on how to handle crashes to make them less dangerous. This could include body position and other things which could potentially make a difference in severity of the cases.
Instant access to medical staff to make any trauma effect less severe.
Direct access to medical staff to analyze the trauma and suggest recovery procedures.
Access to professional staff to maintain and speed up recovery, access to massage.
Protein-rich diet provides building blocks for body to recover faster.
Medical supplements, permitted doping. Good example here with Russian doping scandal related to use of Meldonium. This is a pharmaceutical designed for recovery of damaged by hypoxia heart cells, makes you recover faster after the load. Every professional team has their own set of recovery pharmacy which they would actively use to bring athletes back to business and make them recover ASAP after physical training or trauma.


Personal factors


Pain tolerance and hormonal stimulation. Adrenaline rush in a very competitive race environment is something helping pros to continue the race even after getting some serious trauma.
Very fast methabolism speeds up recovery significantly and allows to utilize more "building blocks" than any average person would.
Psychological factor and motivation. Pros are super motivated to come back to the game and this would make them spend all available time on working to recover from a trauma and go riding as soon as it would be possible and not the hour later. Check this article for the perspective from a pro side of things :)


The world is not just black and white

And last thing, pros are also humans and also suffer from the crashes, so two examples here:


Story from Wikipedia: "Merckx later stated that he "was never the same again" after the crash."
In 2011 Tour De France Johnny Hoogerland had a crash which made him famous but he never fully recovered from it: "Years later, Hoogerland is said to still suffer from back pain, mood swings and insomnia as a result of the horrific incident.".


I hope these thoughts were helpful, keep on recovering after your crash, learn from the pros but take your time :)