I had a similar problem. Rather than an app specific password, I had to append the six digit 'approval' code from my trusted device to my usual password. might be worth a try.

That said, I just tried this. I setup an app-specific password (looks like asdf-asfw-xizx-zxcd) following exactly the instructions at HT204397, in the section titled "Generate an app specific password".



Then I setup Outlook as follows:
File ->Accounts ->New Accounts
Choose "Other".
Enter [email protected] as the email address.
Enter asdf-asfw-xizx-zxcd as the password (This was provided in the Generate step above).
Click Ok.
Done, and I was instantly receiving emails.
That was the fastest email client setup ever. Ever. Nice job, MS.

My account, though uses two-factor auth. Is yours using two-step? According to apple's page, it should work exactly the same way.