Gmail doesn't have a built in way to automatically BCC an email address for each email you send. However, you can use the Chrome extension "Auto BCC for Gmail".
First, you'll want to install the extension AutoBCC for Gmail.
Then you will want to go to this URL to get to the extension settings: chrome-extension://hfjgikgjcgdhlklibkcobckkhklaeodd/options.html
On the settings page, you will want to make sure that "Enable Auto Bcc emails" is checked. Below that, your email address should already be in the "From" section. Then just paste your Parsey mailbox email address into the "Bcc" section and click "Save your Options"
Once you've done that, the Parsey email address will be automatically selected as a Bcc recipient on every email you compose.