See the following from https://support.brother.com/g/s/id/os/macintosh.html
Note: For Windows and Mac (up to Mac OS10.14), any printer will work using the Control Center. There is limited Airprint compatibility if you wish to print from your iPad and iPhone. If you want to print using Airprint printing, please reference the Airprint Compatibility List to check if your printer will work via Airprint on the HMPS1A. Avoid the Apple Brother Printer Update coming via Software Update! My HL-2030 and HL-2035 didn't print anymore with the same symptoms other reviewers reported here. Solution is going to the Brother website (Brother Solutions Center) and download the driver from there. Install on your Mac and it should work again.
The Brother ControlCenter2 is not supported by macOS v10.15.
Download Brother iPrint&Scan for macOS 10.11 or later and enjoy it on your Mac. Brother iPrint&Scan is a free application that lets you easily scan to and print from your Mac. New features are continuously implemented. We recommend periodically checking for updates. For a list of supported models, please visit your local Brother website. If you’re using a Windows PC, download the Control Center 4 Update tool directly from Brother’s website here. If you’re using a Mac computer, it’s important to note that Control Center 4 is a Windows software. It means that the application isn’t suitable for Mac OS. FCB/UnO Control Center lets you manage setups for the original FCB1010 and for the 'UnO equipped' FCB1010. (see www.fcb1010.eu to learn about UnO) Both a native Mac version and a native Windows version are available. The editor design focuses on usability.
Use the Brother iPrint&Scan as an alternative function.
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 4.0 Download
I have a Brother Printer Scanner but I don't have personal experience using the above as I use Apple's Image Capture instead.
Brother Control Center 64 Bit
Oct 21, 2019 2:04 PM