Do most banks run an OFAC check on payees of cashier's checks over a certain dollar amount? If all you have is the payee's name, won't you get a lot of possible matches? How do you deal with that?

We do.
We don't get a lot of possible matches.

We don't check OFAC at the time of issuance, just on our semi-monthly OFAC scrub

I think that is a waste of time as the transaction has already occurred and is out the door. How are you going to prevent the transaction at that point??

We check all bank check payees at the time of check purchase.

Check the payees before issuance. I worked at a small bnak that did it no matter the amount since their volume of checks was low. Current bank performs scans for OFAC for domestic payees of greater than $25k and all foreign payees no matter the amount.

You may want to check with your core processors, as some do it automatically. We use Jack Henry, and as you are typing the payee for the check, it's matching against the OFAC database.