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The Brother Control Center software does not work in Catalina, but Brother printers and scanners continue to work.

I print and scan with my Brother DCP-197C just as I did before.

To scan, I use Preview. File->Import from Brother DCP-197C works fine.

The Brother DCP-L2540DW is fully compatible with Catalina. You can download drivers from the following link. Also note that the replacement for Brother Control Center is their newer iPrint&Scan. You can use that or not, depending on whether you prefer to use Brother utilities or built-in Apple utilities such as Image Capture. See: https://support.brother.com/g/b/downloadlist.aspx?c=us&lang=en&prod=dcpl2540dw_us_as&os=10060

What is the model of your Brother printer?