See the following from https://support.brother.com/g/s/id/os/macintosh.html
DOWNLOAD THE CONTROLCENTER 4 UPDATE TOOL - Download the ControlCenter4 Update Tool from the Brother downloads website - T ype your model number in the field: Search by Model Name, and press Search. On the Select Your Operating System page, simply click on: Search.-Click on the ControlCenter4 Update Tool, under the Utilities section. Very Disappointed with Brother I have owned a number of Brother printers and all-in-ones. My last two have been all-in-ones color laser printers so they are not cheap. I use Macs and up until Catalina - Brother has kept up with the software tools. I very unhappy with Brother for not releasing a 64 bit version of Control Center for Catalina.
The Brother ControlCenter2 is not supported by macOS v10.15.
Brother Control Center Mac Catalina Downloads
Use the Brother iPrint&Scan as an alternative function.
Mac Catalina Download
That can be downloaded from https://help.brother-usa.com/app/answers/detail/a_id/150551/~/download-and-install-brother-iprint%26scan---windows-or-macintosh-computer
Brother Control Center Mac Catalina Download Free
I have a Brother Printer Scanner but I don't have personal experience using the above as I use Apple's Image Capture instead.