$id = "email@example.com"
#See how many items are in mailbox
Get-MailboxFolderStatistics $id | Select Identity, ItemsInFolder
#Delete items in mailbox
Search-Mailbox -Identity $id -DeleteContent -force
"Exchange Server database transaction logs record all changes to an Exchange Server database. Over time, these log files accumulate and use all the available disk space if they are not periodically removed from the hard disk." (ref)By using Scanner, I confirmed that the fat cat on the server was the Exchange logging. For our environment, we didn't care about backing up changes to the database. For this case, enabling circular logging was the solution because it enabled the Exchange server to automatically get rid of unnecessary log files and by so freeing up disk space. I used the directions here to enable circular logging, which involved dismounting and remounting the database.
"To speed up new log file creation and the automatic deletion process, you can send yourself an e-mail message with a 5-megabyte (MB) attachment" (ref)Oddly enough, it worked and shortly thereafter the Exchange server's available disk space increased and the EWS application behaved normally again.