My advice is don’t just ‘blanket letter’ everyone ... there’s soooo many other people doing that ! Research a few practices who you can see have a sense of style that matches where you are heading.
Prepare a letter stating how you like their X project as it echos/complements/was what you were aiming for with the work you have done on Y ( and include images of Y ) add that you feel there could be a benefit for you to learn from their example - if they are willing to allow you to.
Be yourself. Be honest. Don’t brown nose !! Ever !! Honestly - just don’t !!
Best of luck !!! ;-)