Do Brother Scanners run with Big Sur?

It works to some extent if you select macOS 10.14 then 'Scanner Driver'. After installing you can see the scanner in 'Printers & Scanners' then click 'Open Scanner..' A basic scanner app opens. You can scan to PDF etc but each page is saved as a separate file. I'm now on the lookout for some better scanner software that might work with it i.e. able to scan multiple pages into a single document and searchable PDFs etc.

Correction: you can get a driver for Big Sur at the UK Brother site: Downloads & Drivers for ADS-2100e

If that doesn't work, VueScan does support your model. There's a a demo version available to try before you purchase. I've been using it for several years with my scanners and find it to be more powerful than the software that came with my scanners.

The last Image Capture (ICA) scanner driver that Brother posted for this device is in Oct 2020. They could not have tested this will macOS Big Sur (11.0 or later) as the release date was in November. So, if you have installed the version3.3.0 ICA driver and it doesn't work as expected, either Brother will eventually update that ICA driver or you will need to consider trialing and/or purchasing VueScan Professional which drives the ADS-2100e without any Brother software or drivers necessary.