One way to do it is by doing an MX record lookup on the domain (with a fallback to an A record lookup).
I wouldn't do this myself, but have written a post about how to get a mail server's IP address with PHP to help people out should they want to.
As mentioned previously, Laravel will automatically redirect the user back to their previous location.
The class simulates the delivery of a message to see if the given recipient address is accepted as valid.
Seems like everyone and their brother has published one of these.
We're doing the same, combining two different methods we've seen.
A regular expression to match most email addresses, exotic ones would likely be missed.