What to do when two months after submitting a major revision, its status is still "Editor Assigned"?
It's impossible to know what "Editor Assigned" means without knowing the particulars of the journal's system.  I'll presume this is different than what you saw during the prior round of review, however, and it would in fact be unusual for a paper to be stuck with an editor for two months without going out for review.

If you've emailed the handling editor a couple of times at reasonable intervals and gotten not response, then the next step would be to send a polite query to the next level up, which would typically be the chief editors of the journal.  If you get no response there as well, then you've basically got two choices: wait it out some more, or withdraw and submit elsewhere.