Hello @Brendan Short ,
I followed this doc https://learn.microsoft.com/en-us/purview/ediscovery-keyword-queries-and-search-conditions#recipient-expansion AND https://learn.microsoft.com/en-us/purview/ediscovery-kql-editor to try and create a Query that suits your scenario.
Query one:
(Type=Email) AND (Recipients<>"yourdomain.com") AND (HasAttachment=true)
This Query will return Emails that have attachments that are sent to receipts that are not in your domain.
The Documentation doesn't give any direction of getting emails that are specifically sent from your domain. It only gives the option to use Participants which will return messages sent by or sent to a user in the specified domain.
Using this the field will look like below:
(Type=Email) AND (Participants:"your domain" AND Recipients<>"your domain") AND (HasAttachment=true)
I hope this gives you better context on this.