Okay, I created an Outlook email account in Windows 8. It seemed I had no choice. And then, somehow, that seemed to have carried over to the Windows 10 upgrade. I've removed the Microsoft account from my computer and I'm signing in using a local account. So how is Windows 10 checking my Outlook email? I only use the Outlook email account for sites where I don't want to share my main email address. I get a lot of SPAM there and I'm continuously receiving email notifications. I know I can turn off notifications, but how is Microsoft even monitoring that email account?

Your email account resides on a mail server somewhere, and unless you specifically removed it from the server the mailbox will remain active regardless of how you log on to windows.
If you're no longer running an email client program on your windows 10 computer your windows won't be checking the mailbox, but the mailbox will still be able to receive incoming mail to the address.
If you have any webmail access to the email account I'd start by taking a look at the mailbox and what's in it.

I'm just wondering how Microsoft (Windows 10) is checking my Outlook email and notifying me when I have new email when I'm not even logged onto the Outlook account.

I never install windows using an email address and microsoft account, I make sure I just set up a local user. Perhaps if you used the email address in question to setup your windows computer user, that causes automatic email checking? Just a guess.

I guess my specific question is: does anyone know how to prevent Windows 10 from monitoring an Outlook email account?

How to Delete an Email Account from The Mail App in Windows 10:

1.Open Mail app from Start menu. 2.In the bottom left corner, click on the Settings button. 3.From the Settings menu on the right side, click Accounts option. 4.Click on the Account you want to remove. 5.Click on the Delete account option.
Try that

That worked.
Thank you so much, Huw!